To solve the problem of the moving target SAR imaging from an incomplete echo, we proposed a novel SAR imaging method for the moving target with the azimuth missing data (MTIm-AMD). Instead of directly reconstructing the moving target image using the sparse SAR imaging method, we estimate and reconstruct the non-cooperative moving target's complete echo from the azimuth incomplete echo based on its sparsity. At first, the non-cooperative moving target's motion parameters are estimated from the incomplete echo. Then, to ensure that the complete echo can be well reconstructed using the compressed sensing method, these parameters are exploited to design a phase compensation function. Finally, using the reconstructed data, the fine-focused moving target can be obtained via the traditional SAR imaging algorithm. The simulation and experiment data results verify the effectiveness of the proposed MTIm-AMD method and demonstrate that the moving target can be fineimaging when the echo SNR is higher than −20 dB and the azimuth missing ratio (AMR) is less than 70%. This implies that the proposed MTIm-AMD method achieves satisfactory robustness to echo SNR and can handle most AMR cases.