The radar work in a complex environment where the noise has very strong pulse, the noise can be described by stable distribution. The conventional spectrum estimation method based on second order statistics is reasonable in many cases, however, the performance of the conventional algorithm degenerate in stable distribution environment. We propose three new frequency spectrum estimate method with Fractional lower order covariance (FLOC), FLOC-Pisarenko method, FLOC-Esprit method and FLOC multiple signal classification (FLOC-MUSIC) method. The conventional spectrum estimation methods with three proposed methods under Gaussian noise and stable distribution are compared in this paper, simulations show that the conventional methods degenerate, but the proposed algorithms can work better in stable distribution environment, and are robust.