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In 3D face reconstruction, orthogonal projection has been widely employed to substitute perspective projection to simplify the fitting process. This approximation performs well when the distance between camera and face is far enough. However, in some scenarios that the face is very close to camera or moving along the camera axis, the methods suffer from the inaccurate reconstruction and unstable temporal fitting due to the distortion under the perspective projection. In this paper, we aim to address the problem of single-image 3D face reconstruction under perspective projection. Specifically, a deep neural network, Perspective Network (PerspNet), is proposed to simultaneously reconstruct 3D face shape in canonical space and learn the correspondence between 2D pixels and 3D points, by which the 6DoF (6 Degrees of Freedom) face pose can be estimated to represent perspective projection. Besides, we contribute a large ARKitFace dataset to enable the training and evaluation of 3D face reconstruction solutions under the scenarios of perspective projection, which has 902,724 2D facial images with ground-truth 3D face mesh and annotated 6DoF pose parameters. Experimental results show that our approach outperforms current state-of-the-art methods by a significant margin. The code and data are available at https://github.com/cbsropenproject/6dof_face.