Because the performance of traditional Gaussian cognitive radar(CR) system for target response varying from Gaussian will be degraded, this paper extended the Gaussian target response to arbitrary non-Gaussian target distribution. In this paper, the CR multiple hypothesis classification algorithm was used for non-Gaussian targets, and the sparse spectrum of correlated narrowband target responses was utilized. In addition, we simulated the multiple non-Gaussian distribution targets, and the simulation results demonstrate the non-Gaussian target classification algorithm is very effective.