This paper proposes a novel problem-solving strategy for simultaneous escape routing (SER) by imitation learning (IL) which is beneficial to exclude human experts' domain knowledge for designing heuristic solvers. The SER is a crucial task for printed circuit boards (PCB) layout design, affecting signal integrity (SI). However, SER is NP-hard, heuristic solver that provides a fair solution in a reasonable time is needed. We utilize deep neural network (DNN) as a learn-able heuristic solver trained by IL. To be specific, a simple search-based expert policy generates a guiding solution; the DNN learns to imitate the guiding solution. Extensive experiments show that the proposed method significantly outperforms baseline SER methods, including genetic algorithm (GA).