This technical note is concerned with the distributed Kalman filtering problem for a class of networked multi-sensor fusion systems (NMFSs) with missing sensor measurements, random transmission delays and packet dropouts. A novel stochastic model is proposed to describe the transmission delays and packet dropouts, and an optimal distributed fusion Kalman filter (DFKF) is designed based on the optimal fusion criterion weighted by matrices. Some sufficient conditions are derived such that the MSE of the designed DFKF is bounded or convergent. Moreover, steady-state DFKF is also presented for the NMFSs. An illustrative example is given to demonstrate the effectiveness of the proposed results.