As an appealing approach for discovering novel leads, the key advantage of de novo drug design lies in its ability to explore a much broader dimension of chemical space, without being confined to the knowledge of existing compounds. So far many generative models have been described in the literature, which have completely redefined the concept of de novo drug design. However, many of them lack practical value for real-world drug discovery. In this work, we have developed a graph-based generative model within a reinforcement learning framework, namely METEOR (Molecular Exploration Through multiplE-Objective Reinforcement). The backend agent of METEOR is based on the well-established GCPN model. To ensure the overall quality of the generated molecular graphs, we implemented a set of rules to identify and exclude undesired substructures. Importantly, METEOR is designed to conduct multi-objective optimization, i.e. simultaneously optimizing binding affinity, drug-likeness, and synthetic accessibility of the generated molecules under the guidance of a special reward function. We demonstrate in a specific test case that, without prior knowledge of true binders to the chosen target protein, METERO generated molecules with superior properties compared to those in the ZINC 250k data set. In conclusion, we have demonstrated the potential of METERO as a practical tool for generating rational drug-like molecules in the early phase of drug discovery.