In order to improve the direction-of-arrival (DOA) estimation performance of quasi-stationary signals (QSS) using a uniform circular array (UCA), this paper addresses novel method in the context of sparse representation framework. Based on the Khatri-Rao transform, UCA can achieve a higher number of degrees of freedom to resolve more signals than the number of sensors. Then, by exploiting the two-dimensional (2-D) joint grid of UCA, the estimations of elevation and azimuth angles can be obtained from the sparse representation perspective. Finally, an expectation-maximization iteration method is developed to estimate DOAs of QSS from a Bayesian perspective. Since SBL makes full use of the sparse structure of QSS, thus the proposed algorithm possesses higher angular resolution and better DOA estimation precision compared with existing methods. Numerical simulations demonstrate the validity of the proposed method.