After trying many times, i wrote this script. It finally solved my problems which i just want to correct the wrong vertex and remain the right ones. Only the wrong vertex coordinates in point table. 

    import arcpy
    from arcpy import env
    env.overwriteOutput = True
    env.workspace = "E:\\test"

    points = "point.shp"
    lines = "merge_line.shp"
    point_id_field = 'station_id'

    points_cursor = arcpy.da.SearchCursor(points, [point_id_field, 'SHAPE@X','SHAPE@Y'])
    points_dict={}
    for points_row in points_cursor:
        station_id = points_row[0]
        x = points_row[1]
        y = points_row[2]
        points_dict[str(int(station_id))] = str(x),str(y)
    with arcpy.da.UpdateCursor(lines,["From_id","To_id","OID@","SHAPE@"]) as update_cursor:
        for update_row in update_cursor:
            print("Feature{0}:".format(update_row[2]))
            from_id = update_row[0]
            to_id = update_row[1]
            if from_id in points_dict.keys() and to_id not in points_dict.keys():
                print from_id
                geometry = update_row[3]
                pts = geometry.getPart(0)
                n = len(pts)
                pt_array1 = arcpy.Array()
                for i in xrange(n):
                    if i == 0:
                        frompoint1 = pts.getObject(i)
                        print frompoint1.X, frompoint1.Y
                        frompoint1.X = points_dict[from_id][0]
                        frompoint1.Y = points_dict[from_id][1]
                        print frompoint1.X ,frompoint1.Y
                        pt_array1.add(frompoint1)
                    
                    elif i == 1:
                        topoint1 = pts.getObject(i)
                        print topoint1.X,topoint1.Y
                        pt_array1.add(topoint1)
                new_polyline_geometry = arcpy.Polyline(pt_array1)        
                update_row[3] = new_polyline_geometry
                update_cursor.updateRow(update_row)        
            elif from_id in points_dict.keys() and to_id in points_dict.keys():
                print from_id, to_id
                geometry = update_row[3]
                pts = geometry.getPart(0)
                n = len(pts)
                pt_array2 = arcpy.Array()
                for i in xrange(n):
                    if i == 0:
                        frompoint2 = pts.getObject(i)
                        print frompoint2.X, frompoint2.Y
                        frompoint2.X = points_dict[from_id][0]
                        frompoint2.Y = points_dict[from_id][1]
                        print frompoint2.X ,frompoint2.Y
                        pt_array2.add(frompoint2)
                    elif i == 1:
                        topoint2 = pts.getObject(i)
                        print topoint2.X, topoint2.Y
                        topoint2.X = points_dict[to_id][0]
                        topoint2.Y = points_dict[to_id][1]
                        print topoint2.X, topoint2.Y
                        pt_array2.add(topoint2)
                new_polyline_geometry = arcpy.Polyline(pt_array2)        
                update_row[3] = new_polyline_geometry
                update_cursor.updateRow(update_row)
            elif to_id in points_dict.keys() and from_id not in points_dict.keys():
                print to_id
                geometry = update_row[3]
                pts = geometry.getPart(0)
                n = len(pts)
                pt_array3 = arcpy.Array()
                for i in xrange(n):
                    if i == 0:
                        frompoint3 = pts.getObject(i)
                        print frompoint3.X,frompoint3.Y
                        pt_array3.add(frompoint3)
                    if i == 1:
                        topoint3 = pts.getObject(i)
                        print topoint3.X, topoint3.Y
                        topoint3.X = points_dict[to_id][0]
                        topoint3.Y = points_dict[to_id][1]
                        print topoint3.X, topoint3.Y
                        pt_array3.add(topoint3)
                new_polyline_geometry = arcpy.Polyline(pt_array3)        
                update_row[3] = new_polyline_geometry
                update_cursor.updateRow(update_row)