A method of composing and displaying screen images includes transmitting a screen image of a guest operating system (OS) to a host OS, in response to the guest OS and the host OS exclusively or jointly accessing a graphics processing unit (GPU) in a pass-through or mediated pass-through environment via GPU virtualization; generating a composition screen image by transforming the screen image of the guest OS into a texture and composing the texture with a texture screen image of the host OS; and displaying the composition screen image.