This paper develops a novel off-policy Q-learning method for solving linear quadratic tracking (LQT) problem in discrete-time networked control systems with packet dropout. The proposed method can be implemented using measured data without requiring systems dynamics to be known a priori, and it also allows bounded packet loss. First, networked control systems with packet dropout are established, thus an optimal tracking problem of linear discrete-time networked control systems is further formulated. Then, a Smith predictor is designed to predict current state based on historical data measured on the communication network. On this basis, an optimal tracking problem with packet dropout compensation is put up. Finally, a novel off-policy Q-learning algorithm is developed by integrating dynamic programming with reinforcement learning. The merit of the proposed algorithm is that the optimal tracking control law based predicted states of systems can be learned using only measured data without the need of knowing system dynamics. Moreover, the unbiasedness of solution to Q-function based Bellman equation can be guaranteed by using off-policy Q-learning approach. The simulation results show that the proposed method has good tracking performance for the network control system with unknown dynamic state and packet dropout.