Circuit simulation has become increasingly significant in circuit design with the development of very large scale integration, and direct current (DC) analysis, which serves as the basis of circuit behavior analysis, is the foundation for nonlinear electronic circuit simulation. Among the several continuation algorithms for DC analysis, pseudo-transient analysis (PTA) methods have gained great success. However, PTA tends to be computationally intensive without a proper time-step control method. In order to improve this problem, we propose a novel time-step control method enhanced by advanced deep learning in this paper. Specifically, a coarse and fine-grained hybrid sampling strategy is introduced to find the optimal time step, which resolves the problem that the optimal time step has no precise definition in PTA theory. After that, a long short-term memory (LSTM) network, with the ability to process temporal information, can be employed to learn the optimal time-step control method based on feature selection and a two-stage data preprocessing strategy, which accelerates DC analysis. Furthermore, random forest (RF) is also used to evaluate feature importance, which can achieve feature selection with reduced dimensions, thereby speeding up the network’s training speed and improving the accuracy of prediction. Experimental results demonstrate a significant speedup: up to 61.32 times.