Mask three-dimensional (M3D) effects are non-negligible for imaging simulation of EUV lithography systems. Especially, the curvilinear mask obtained by inverse lithography technique (ILT) increases the difficulty to calculate the diffraction spectrum of the thick masks. In this paper, a fast thick-mask model based on multi-channel U-Net (MCU-Net) is proposed to solve this problem. The diffraction near-field (DNF) of thick mask in EUV lithography is characterized by four complex-valued diffraction matrices, the real parts and imagery parts of which can be represented by eight realvalued diffraction matrices in total. Then, all of the eight real-valued diffraction matrices can be synthesized together using the proposed MCU-Net model. The parameters of MCU-Net are trained in a supervised manner based on a precalculated DNF dataset of curvilinear thick masks. The comparison of the proposed method with some other learningbased thick-mask models is provided and discussed. It shows that the MCU-Net is efficient and accurate to simulation the M3D effect in EUV lithography.