This paper proposes a fast simulation method for the three-dimensional (3D) contact hole mask in extreme-ultraviolet lithography. Using the mask diffraction simplified model, an analytical expression of the diffraction spectrum of the contact hole is given, and theory analysis of the pattern shift effect is performed. The mask in the model includes two parts, the absorber and the multilayer structure. The absorber transmission is calculated using the modified thin mask model, and the multilayer reflection is approximated as mirror reflection. Taking 16 nm and 22 nm contact holes with a pitch of 44 nm as examples, the critical dimensional errors of the model are below 0.4 nm by comparison with the rigorous simulations, and the computation speed is increased nearly 100 times. Moreover, considering the equivalent location of the multilayer in the model, a formula is derived to calculate the amount of the pattern shift. The calculation results are consistent with those of the rigorous simulations as well.