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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

enter image description here

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:

enter image description here

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)

  • @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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