Azimuth super-resolution has always been a hot research topic in radar domain.For the ill-condition encountered in the solving process,a thorough analysis is made of L1 norm regularization method and its constrained method.Under the premise of the target sparse nature,L1 norm regularization model and its constrained model are established,and a gradient projection algorithm is used to solve them for the large dimensions of radar data.A computer simulation for two equal amplitude point targets is made at different Signal-to-Noise Ratios (SNRs).The preliminary findings show that:1) with the decease of SNR,the resolution effect of both algorithms becomes worse,of which,the constrained L1 norm regularization method has a relatively better resolution under the same condition,and can distinguish the two equal amplitude point targets with a interval of 1/2 half power beam width when SNR is 0 dB;2) the constrained method has a better performance in resolution than L1 norm regularization method,constrained iterative deconvolution algorithm,wiener inverse filter algorithm and Richardson-Lucy algorithm (RL algorithm);and 3) these two norm regularization methods have stronger noise adoptability,which can be used for radar azimuth super-resolution.