The state estimation problem of stochastic uncertain systems with missing measurements is studied. A group of Bernoulli distributed random variables is employed to describe the phenomenon of packet dropouts, and the predictor of lost observation is used as the observation when a packet is lost. The optimization problem under uncertain conditions is described as a Min-Max problem, by using two groups of Lagrange multipliers, the Min-Max problem is transformed into a constrained Min-Min problem, and then the optimal estimator is obtained. The stability of the proposed algorithm is studied, the upper bound of the expectation of the square norm of estimation error is obtained, and a sufficient condition for the convergence of the square norm of estimation error is given. Finally, an example is given to demonstrate the effectiveness of the proposed method.