The azimuth resolution of civil navigation radar depends on the size of antenna aperture. Large aperture antenna is restricted by many factors in engineering project, and it is difficult to be widely used. For this problem a super-resolution method based on Lagrange theory is proposed in this paper. The convolutional echo is converted into the form of matrix-vector product by supplementing elements to azimuth signal vector. Combining singular value decomposition (SVD) to antenna pattern with BFGS algorithm a new observed model is established, and Lagrange function is utilized to solve the new model for restoring original azimuth signals, by which azimuth super-resolution can be realized. Experimental performances manifest that the proposed method has good super-resolution, and a higher signal reconstruction to error ratio (SRER) is obtained comparing with dual-logarithmic method while the signal to noise ratio (SNR) ranges from 10dB to 20 dB.