Can I use a monitor for both my laptop and my Xbox 360?

So I currently have a laptop with a really small screen, so I have a monitor that is connected to it via the Blue VGI cable.  I plan on buying another moniter with a VGI and two HDMI inputs for an Xbox 360.  So basically my question is, Can I use the Moniter Duel Monitering the Laptop with the VGI Cable, and use the HDMI of the Moniter to connect it to the Xbox?  I know for a fact everything will be plugged in, just want to know if I can use it for both.  Like whenever I want to use the monitor with the laptop, I'll have it with that.  And when I want to use it for xbox, I can.  And if I can quickly switch it back over for use with the Laptop and switch it back with the Xbox still running to be back on Xbox.

I think you mean VGA, not VGI...anyway if the new monitor has multiple inputs (VGA plus 2 HDMI) then the monitor should be able to switch between the inputs at will....so...yes....