A method using a calibration device consisting of two orthogonal planes was proposed to address the moving direction calibration problem for 2D LiDAR mounted on a linearly moving platform. When the linearly moving 2D LiDAR performs two or more scans of the calibration device, geometric constraints on the motion parameters can be derived from the scan lines on the two calibration planes. The parameters must lie on a hyperbola on the parameter plane. Additional constraint hyperbolas are generated by adjusting the pose of the calibration device and conducting new scans. To solve the calibration problem, four algorithms were presented: Linear least squares method (LSM), Gauss-Newton method (G-N) and an optimization approach that minimizes the sum of squared shortest distances from a point to all constraint curves (denoted as Opt-D), as well as a method that optimizes the orthogonality of the reconstructed calibration planes (denoted as Opt-O). Simulation experiments demonstrated that the Opt-O method achieves the highest accuracy. In real experiments, a 3D point cloud of a plastic ball was constructed from the calibration results and was used to estimate the spherical equation. When using the results of G-N, Opt-D, or Opt-O methods, the mean distances between the reconstructed sampled points and the fitted sphere are all less than 0.5 mm, with the standard deviations all less than 0.5 mm. These results collectively validate the effectiveness of the proposed calibration method.