Ghost imaging LiDAR via sparsity constraints using push-broom scanning is proposed. It can image the stationary target scene continuously along the scanning direction by taking advantage of the relative movement between the platform and the target scene. Compared to conventional ghost imaging LiDAR that requires multiple speckle patterns staring the target, ghost imaging LiDAR via sparsity constraints using push-broom scanning not only simplifies the imaging system, but also reduces the sampling number. Numerical simulations and experiments have demonstrated its efficiency.