The "left socket" you mention is of the opposite gender and is used as a power output for a monitor - it can't be used as input. You have to use the right socket regardless of voltage.
It's not uncommon for old PC power supplies to lack a voltage selection switch and just accept a single input voltage, unfortunately yours seem to be one of those, and it doesn't match your local electric supply. Due to the nature of the power supplies from that era it's almost certain that if you connect your computer directly to the wall, the power supply will go up in smoke.

If you are not well versed in electronics your options are:

• Replace the power supply with one that is set for 220V AC input.
• Use the computer plugged into a 220-110V step-down autotransformer, with at least a 200VA power rating (conservative).

If you are knowledgeable in electronics and qualified to safely work inside AC line powered equipment:

• Sometimes the voltage selecion is internal in the shape of a jumper wire you need to cut/join to switch between 220/110V operation, which may or may not be conveniently labeled.
• If there are two smoothing capacitors on the primary side the PSU is most likely using a voltage doubler configuration to boost up the rectified 110VAC mains to ~340VDC, if that's the case the voltage doubler can be undone into a simple rectifier for 220VAC operation - if there is a bridge rectifier onboard it should be as simple as cutting two tracks and adding a jumper in the right place (and maybe replacing an MOV or two).

Use the computer plugged into a 220-110V step-down autotransformer, with at least a 200VA power rating (conservative).

That's a good idea. But be careful with cheap converters. Make sure they say "for computer use" or something like that.
Strong switching-PSUs expect still to be fed by clean, sine-shaped AC, I believe.
Back in time, when average switching-transformers were still producing something that rather looked like sawtooth,
such devices required a real step-down transformer, made of copper wire.

Jo22 wrote:

That's a good idea. But be careful with cheap converters. Make sure they say "for computer use" or something like that. Strong s […]
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That's a good idea. But be careful with cheap converters. Make sure they say "for computer use" or something like that.
Strong switching-PSUs expect still to be fed by clean, sine-shaped AC, I believe.
Back in time, when average switching-transformers were still producing something that rather looked like sawtooth,
such devices required a real step-down transformer, made of copper wire.

Using an autotransformer, this shouldn't be a problem unless the core is massively underspecified (where you'll get saturation distortion). Different story with transistor, thyristor, or tube based converters, of course.

Thanks for the reply everyone!

After seeking for a similar XT power supply which equipped with voltage selection on the back for weeks, I decide to get a step-down transformer for running it.
It's too hard to get a 220V XT power supply which fits to be installed in the chassis.