Problem in star delta starter in air compressor
Above diagram shows V1 and V2 connected to same phase through the main contactor and delta contactor. 
  But,This diagram is wrong according to my real connection.


You are correct. The diagram is wrong.



Figure 1. Here is the same crude drawing but the phase sequence is correct and somebody has coloured it up. Source: Electrical Notes.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. Drawing of your wiring looks OK.


  I didn't check the winding of the motor. I trusted the tag on the wire.


Very foolish.

The panel wiring in your photo is atrocious. It needs a major tidy up.