I guess, there have been 25 or more working 4 to 20 mA I/V converters posted at edaboard during the last years. Why did you design a new non working?
Problems involved with your design:
- it has to connect the negative current source output to the amplifier and the positive to ground, opposite to the industry standard. If any standard equipment has to be connected, you would want a positive current input.
- the circuit doesn't implement the necessary offset to get 0V at 4 mA.
I suggest a 50 or 100 ohm shunt with a suceeding differential amplifier, it can provide the factor 5 or 10 gain along with the offset. A stable reference voltage will be needed for this purpose. If you think your VCC supply is stable enough for this purpose, you have to tell the voltage, a least.
P.S.: It would be a good idea to post images in a compressed (gif or jpg format) to save server space and download time. Even the trivial Windows Paint tool can convert it.