Intelligent manipulation of robots in an unstructured environment is an important application field of artificial intelligence, which means that robots must have the ability of autonomous cognition and decision-making. A typical example of this type of environment is a cluttered scene where objects are stacked and close together. In clutter, the target(s) may be one or more, and efficiently completing the target(s) grasping task is challenging. In this study, an efficient push-grasping method based on reinforcement learning is proposed for multiple target objects in clutter. The key point of this method is to consider the states of all the targets so that the pushing action can expand the grasping space of all targets as much as possible to achieve the minimum total number of pushing and grasping actions and then improve the efficiency of the whole system. At this point, we adopted the mask fusion of multiple targets, clearly defined the concept of graspable probability, and provided the reward mechanism of multi-target push-grasping. Experiments were conducted in both the simulation and real systems. The experimental results indicated that, compared with other methods, the proposed method performed better for multiple target objects and a single target in clutter. It is worth noting that our policy was only trained under simulation, which was then transferred to the real system without retraining or fine-tuning.