Employing unmanned aerial vehicles (UAVs) has attracted growing interests and emerged as the state-of-the-art technology for data collection in Internet-of-Things (IoT) networks. In this paper, with the objective of minimizing the total energy consumption of the UAV-IoT system, we formulate the problem of jointly designing the UAV's trajectory and selecting cluster heads in the IoT network as a constrained combinatorial optimization problem which is classified as NP-hard and challenging to solve. We propose a novel deep reinforcement learning (DRL) with a sequential model strategy that can effectively learn the policy represented by a sequence-to-sequence neural network for the UAV's trajectory design in an unsupervised manner. Through extensive simulations, the obtained results show that the proposed DRL method can find the UAV's trajectory that requires much less energy consumption when compared to other baseline algorithms and achieves close-to-optimal performance. In addition, simulation results show that the trained model by our proposed DRL algorithm has an excellent generalization ability to larger problem sizes without the need to retrain the model.