The problem of delay-dependent robust stability for a class of discrete-time uncertain singular Markovian jump systems with interval time-varying delay is studied. By combining the Jensen inequality with a new bounding inequality, a novel stability criterion is obtained, which involves only Lyapunov variables and has less computation burden. Based on the convex combination method, another novel stability criterion is proposed, which introduces some free matrix variables and is less conservative. Numerical examples show the effectiveness of the proposed approach.