To meet the request of high resolution on cross-track, conventional downward-looking three-dimensional synthetic aperture radar (DL 3D SAR) imaging on micro unmanned aerial vehicle requires much longer transmitting antenna and more receiving antenna array. A novel imaging method of DL 3D SAR based on Lp regularization is proposed. Analyzing the 3D echo signal model, the over-complete dictionary is structured. And the imaging problem is transformed into a Lp regularization model which can be solved by sparse Bayesian learning method. The simulation results show that the proposed method can cut down nearly 3/4 length of antenna array without reducing the imaging quality obviously, or make the cross-track resolution improve 2 times with full sampling compared to the conventional method.