You could use a low-drop-regulator, but it would help if you specify the maximum drawn current. Maximum current for LM317T is 1.5A. Do you really need that ?
For a voltage as low as 3V, and using LM317, I would not be very happy with the regulation of the prresent circuit.
I would use an external op-amp and employ -ve feedback fot much tighter voltage regulation.
the problem is that the output is not sharp 3V... tolerance are small for my device and the error in this circuit is not controlled... some times E=30%... too much! the variable resistance solving the problem of R error... (100:140 is the ratio between R1 and R2)...
so do any one have alternative circuit to produce 500 mA (or highr) and have high effeciency?
I think you can try the following arranged to its cost
1- use metal film resistors to set the adjust pin voltage as carbon film resistors has big error compared to the precsion you need and the pot always cause high drift.
2- use some kind of feed back to monitor the output voltage.
3- Use current posting transistor, if your circuit draws high currnt that cause heeat dissipation in regulator that make its output drift (refer to data shhets).