As the technology node shrinks to the nanometer regime, the demand for new lithography methods with high resolution and low cost is increasing. Electron beam lithography (EBL) is one of the promising next-generation lithography (NGL) technologies that can tackle both challenges compared to the traditional lithography methods. Fogging effect, a culprit of pattern distortion in layout, is one of the major challenges that prevent industry from adopting EBL in technologies below 22nm. This paper proposes a reinforcement-learning (RL) placement method that trains a neural network as an agent to effectively control fogging effect. To speed up our method, we benefit from the following innovations: using topological floorplan representation for the layouts during placement, and deploying a RL trained agent that can intelligently take actions. The experimental results show that our proposed placer is able to more effectively and efficiently reduce the fogging effect variation in the analog circuits in comparison with the conventional simulated-annealing-based placement method.