When transferring a Deep Reinforcement Learning (DRL) model from simulation to the real world, the performance could be unsatisfactory since the simulation cannot imitate the real world well in many circumstances. This results in a long period of fine-tuning in the real world. This paper proposes a self-supervised vision-based DRL method that allows robots to pick and place objects effectively and efficiently when directly transferring a training model from simulation to the real world. A height-sensitive action policy is specially designed for the proposed method to deal with crowded and stacked objects in challenging environments. The training model with the proposed approach can be applied directly to a real suction task without any fine-tuning from the real world while maintaining a high suction success rate. It is also validated that our model can be deployed to suction novel objects in a real experiment with a suction success rate of 90\% without any real-world fine-tuning. The experimental video is available at: \url{https://youtu.be/CVcvIg62Iww}.