A novel direction-of-arrival (DOA) estimation method is proposed based on the sparse cumulants fitting without redundancy. Firstly, we derive that some fourth order cumulants of the array output are redundant and therefore are removed to reduce computational complexity. Then, the left cumulants are sparsely represented on an overcomplete basis and the DOAs are resolved by using a software package. Despite introducing a high variance, the proposed method shows several advantages including the ability to detect more sources than sensors, high resolution, and robustness to all kinds of Gaussian noise. Besides, our method does not have to know, a priori, the number of sources. Simulation results are presented to illustrate the effectiveness and efficiency of the proposed method.