In this paper, the problem of trajectory design of unmanned aerial vehicles (UAVs) for maximizing the number of satisfied users is studied in a UAV based cellular network where the UAV works as a flying base station that serves users, and the user indicates its satisfaction in terms of completion of its data request within an allowable maximum waiting time. The trajectory design is formulated as an optimization problem whose goal is to maximize the number of satisfied users. To solve this problem, a machine learning framework based on double Q-learning algorithm is proposed. The algorithm enables the UAV to find the optimal trajectory that maximizes the number of satisfied users. Compared to the traditional learning algorithms, such as Q-learning that selects and evaluates the action using the same Q-table, the proposed algorithm can decouple the selection from the evaluation, therefore avoid overestimation which leads to sub-optimal policies. Simulation results show that the proposed algorithm can achieve up to 19.4% and 14.1% gains in terms of the number of satisfied users compared to random algorithm and Q-learning algorithm.