Could it cause electrical hazard if I connect as diagram below?

Hello,
I need to use 220VAC to connect DC power supply. As you can see it is center tapped transformer and ground is connected with center tap. Would it be fine to connect X1 with L, X4 with N and ground with G on DC power supply? What would be the safe way to wire to use both 110V and 220V?

The wiring diagram looks fine to me. The way it is supposed to be connected.

Not sure what you mean by using 120 and 220 at the same time though.

Need model number of power supply. Is it a SMPS? Some expect the N side to be at a low potential.

Your drawing depicts a normal 120/240V distribution.
If your power supply is rated for 100-240V as many are it should be fine.