Airborne radars usually face non-uniform clutter environments, and it is difficult to obtain enough independent and identical distributed (i.i.d.) training samples, which degrades the clutter suppression performance of space time adaptive processing (STAP). To address the problem, a log-determinant sparse rocovery based STAP (LSR-STAP) method is proposed in this paper. Through the sparse recovery theory of low-rank matrices and the prior knowledge of clutter covariance matrices, the corresponding problem is modeled using the log-determinant (LogDet) approximation of the rank function, and the solution of the resulting nonconvex optimization problem is derived in the framework of the symmetric alternating direction method of multipliers (S-ADMM). The simulation results show the superiority of the proposed method over similar algorithms.