The invention provides a method and a system for estimating the direction of arrival of correlated signals based on a co-prime array. The method includes the following steps: signals received by a co-prime array are sampled to get time-domain discrete signals; the fourth-order cumulants of sub-array signals are obtained by setting the number of array elements of sub-arrays according to the time-domain discrete signals, and the fourth-order cumulants of sub-array signals are smoothed forward and backward to obtain smoothed fourth-order cumulants; eigenvalue decomposition is carried out on the smoothed fourth-order cumulants to obtain projection operators; and finally, the direction of arrival of the signals is estimated by using a Root-MUSIC algorithm according to all the projection operators. According to the method and the system, the direction of arrival of the signals is estimated by combining a co-prime array and fourth-order cumulants. The accuracy of the estimation result can beensured without increasing the number of array elements, and a better effect can be achieved when the number of signals is greater than the number of array elements. Moreover, signal correlation can be relieved, the spatial resolution of signals is enhanced, and the method and the system can be applied to various complex environments.