Traditional cortical surface reconstruction is time consuming and limited by the resolution of brain Magnetic Resonance Imaging (MRI). In this work, we introduce Pial Neural Network (PialNN), a 3D deep learning framework for pial surface reconstruction. PialNN is trained end-to-end to deform an initial white matter surface to a target pial surface by a sequence of learned deformation blocks. A local convolutional operation is incorporated in each block to capture the multi-scale MRI information of each vertex and its neighborhood. This is fast and memory-efficient, which allows reconstructing a pial surface mesh with 150k vertices in one second. The performance is evaluated on the Human Connectome Project (HCP) dataset including T1-weighted MRI scans of 300 subjects. The experimental results demonstrate that PialNN reduces the geometric error of the predicted pial surface by 30% compared to state-of-the-art deep learning approaches. The codes are publicly available at https://github.com/m-qiang/PialNN.