In this paper, we propose the Uzawa splitting iteration method for solving a class of singular saddle point problems. The semi-convergence of the Uzawa splitting iteration method is carefully analyzed, which shows that the iteration sequence generated by this method converges to a solution of the singular saddle point problems under certain conditions. Moreover, the characteristics of the eigenvalues and eigenvectors of the iteration matrix of the proposed method are studied. The theoretical results are supported by the numerical experiments, which implies that Uzawa splitting iteration method is effective and feasible for solving singular saddle point problems.