Hello,
I built the power supply from the attached schematic.
I found that the output voltage, measured between GND and the output pin of LM317 (pin 2) drops by 0.28V while powering a 2.9A load.
It is normal to drop by such a high value ?
The schematic is not mine, it has been taken from a forum.

Later Edit: The maximum output current has been set to 4A before connecting the load. The red led does not lit while powering the load.

 

I found that the output voltage, measured between GND and the output pin of LM317 (pin 2) drops by 0.28V while powering a 2.9A load.

That drop is likely due to wire resistance between the LM317 and the output.
To minimize the drop at the load, connect the LM317 output pin directly to the supply output terminal with a large gauge, short wire, and connect the bottom of the voltage reference resistor (I think R13 in your schematic) directly to the supply output common terminal.