A learning-based self-calibration method is demonstrated to achieve simultaneous corrections for both lateral and axial field distortions in three-dimensional (3D) surface topography measurements. In this method, the back propagation neural network is introduced into the self-calibration technology to learn the mapping relationship between the distorted space and the undistorted space for realizing the separation of systematic errors and calibration sample topography. The rigid body feature of the artifact is used to construct the loss function to achieve the optimization of network parameters. This method not only retains the advantages of the self-calibration method but also characterizes a complex distortion model. Simulation results show that the accuracy of nanometers is achieved for the correction of lateral and axial field distortions. In the experiment, the root-mean-square (RMS) values of lateral correction residual errors are less than 30 nm, and the axial RMS values are less than 2 nm. Simulation and experimental results prove that this method can correct both lateral and axial field distortions to the level of nanometer by one calibration. It indicates that the learning-based self-calibration method might be the future development trend for lateral and axial field distortions corrections of measuring instruments in 3D surface topography measurement.