1. A method of composing and displaying screen images, implemented by at least one processor, the method comprising: 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 mediated pass-through environment via GPU virtualization; adjusting a scheduling priority of the GPU for the guest OS and the host OS based on a comparison between a target frames per second (FPS) and a current FPS of the guest OS and the host OS; generating a composition screen image by copying the screen image stored in a first storage area of the guest OS to a second storage area of the host OS in response to receiving a storage completion signal for the screen image of the guest OS from the guest OS and 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, wherein the generating the composition screen image comprises, in response to a format of the screen image of the guest OS being different from a format of the texture screen image of the host OS, transforming the format of the screen image of the guest OS into a format of the host OS to generate the texture.