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Under-Display Camera (UDC) has been widely exploited to help smartphones realize full screen display. However, as the screen could inevitably affect the light propagation process, the images captured by the UDC system usually contain flare, haze, blur, and noise. Particularly, flare and blur in UDC images could severely deteriorate the user experience in high dynamic range (HDR) scenes. In this paper, we propose a new deep model, namely UDC-UNet, to address the UDC image restoration problem with the known Point Spread Function (PSF) in HDR scenes. On the premise that Point Spread Function (PSF) of the UDC system is known, we treat UDC image restoration as a non-blind image restoration problem and propose a novel learning-based approach. Our network consists of three parts, including a U-shape base network to utilize multi-scale information, a condition branch to perform spatially variant modulation, and a kernel branch to provide the prior knowledge of the given PSF. According to the characteristics of HDR data, we additionally design a tone mapping loss to stabilize network optimization and achieve better visual quality. Experimental results show that the proposed UDC-UNet outperforms the state-of-the-art methods in quantitative and qualitative comparisons. Our approach won the second place in the UDC image restoration track of MIPI challenge. Codes will be publicly available.