A fast simulation method based on variable separation is proposed for 3D mask diffraction in extreme-ultraviolet lithography (EUVL). The method achieves higher simulation speed while maintaining a good simulation accuracy. In this method, the 3D mask is decomposed into two orthogonal 2D masks. The diffraction spectrum simulation on two 2D masks are carried out through rigorous electromagnetic method. The results are then multiplied to reconstruct the three-dimensional diffraction spectrum. We set a premise of 6° main incident angle, 45° linearly polarized light illumination and 22 nm 3D square contact hole mask. Azimuth angle is ranging from 0° to 90°. Under the same simulation parameters, the simulation results of this method are compared with the rigorous simulation results of commercial lithography simulation software Dr.LiTHO. The errors of the simulated critical-dimension of the proposed method are within 0.21 nm, and the simulation speed is about 65 times faster. Under the above parameters, the proposed method is compared with the domain decomposition method of Dr.LiTHO and a fast method based on mask-structure decomposition. The results show that the simulation accuracy and speed are improved more than double. The method needs no calibrations for model parameters and suits fast simulations of 3D masks that contain rectangular patterns.