Recently, curvature filter (CF) has been developed to implicitly minimize curvature for image processing problems such as smoothing and denoising. In this paper, we propose a parallel curvature filter (PCF) that performs on GPU which is much faster than the original CF on CPU. Inspired by Convolution Neural Networks processed by GPU, the convolution operations in curvature filter computation can be similarly paralleled by GPU so that the PCF on a single GPU can process 33.2 Giga pixels per second.