The discrete-time state estimation problem is studied for networked control systems subject to random network delays without time stamping. A new time delay model is presented which allows the transmitted data to be received in bursts. Under the assumption that the data bursts are not out of order, we derive the optimal linear estimator which guarantees an unbiased estimate with minimum and uniformly bounded estimation error covariance. The estimator gains can be derived by solving a set of recursive discrete-time Riccati equations. A simulation example shows the effectiveness of the proposed algorithm.