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Is there anyway to determine projection of a shapefile which doesn't have .prj file?

I am trying to re-project this shapefile to another projection, I know that it is Lat long data. I could manage to load this in GIS tools like this or QGIS

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Based on DBF data, it's Auckland data. According to this link the EPSG code of New Zealand is 27120 as the picture indicates:

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Also I tried to display a point of this shape in Google Maps and it worked:

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But still not sure what is the projection of this shapefile? I don't think it's WGS84 because I wasn't successful to reproject it from WGS84 to EPSG:27120 which is New Zealand grid system.

If it's not WGS84 how does Google display the point successfully?

The shapefile is available here, it is small (5KB)

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  • @Joseph Thank you very much. Maybe you can post it as answer then I can mark it as accepted. The problem was choosing wrong projection for destination projection.
    – Shahin
    Mar 19 '15 at 15:08
  • Most welcome buddy! I posted the comment as an answer and I'm glad you got it sorted :)
    – Joseph
    Mar 19 '15 at 15:16
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I'm not sure how you can obtain a shapefiles initial CRS but you can reproject your shapefile to another New Zealand grid system (EPSG:27200 - NZGD49 / New Zealand Map Grid) via the Save As... option.

I used QGIS 2.6.1 to successfully reproject the shapefile:

Projected shapefile

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