I am trying to make a shield for Arduino DUE. As the supply is already regulated, do I need to add the extra capacitor. Please find the attachment.
It depends on what is the power supply... It might be a wall wart or a power supply board, in that case, they should already have these capacitors and if the wire is not too long, I don't think you have to add another couple of capacitors.
If it comes from an IC on your board then you should add them.
You always need to add a 0.1 uF capacitor as close to the pins on the chip as possible, no matter what you are making.