This technical note studies some of the challenging issues on moving horizon state estimation for networked control systems in the presence of multiple packet dropouts in both sensor-to-controller and controller-to-actuator channels, which both situations are modeled by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. Compared with standard Kalman filter, this study proposes a novel moving horizon estimator to deal with the uncertainties induced from the multiple packet dropouts, which has a larger degree of freedom to obtain better behavior by tuning the weight parameters. A sufficient condition for the convergence of the norm of the average estimation error is also presented to guarantee the performance of the estimator. Finally, a real-time simulation experiment is presented to demonstrate the feasibility and efficiency of the proposed method.