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Directed Greybox Fuzzing (DGF) is an effective approach designed to strengthen testing vulnerable code areas via predefined target sites. The state-of-the-art DGF techniques redefine and optimize the fitness metric to reach the target sites precisely and quickly. However, optimizations for fitness metrics are mainly based on heuristic algorithms, which usually rely on historical execution information and lack foresight on paths that have not been exercised yet. Thus, those hard-to-execute paths with complex constraints would hinder DGF from reaching the targets, making DGF less efficient. In this paper, we propose DeepGo, a predictive directed greybox fuzzer that can combine historical and predicted information to steer DGF to reach the target site via an optimal path. We first propose the path transition model, which models DGF as a process of reaching the target site through specific path transition sequences. The new seed generated by mutation would cause the path transition, and the path corresponding to the high-reward path transition sequence indicates a high likelihood of reaching the target site through it. Then, to predict the path transitions and the corresponding rewards, we use deep neural networks to construct a Virtual Ensemble Environment (VEE), which gradually imitates the path transition model and predicts the rewards of path transitions that have not been taken yet. To determine the optimal path, we develop a Reinforcement Learning for Fuzzing (RLF) model to generate the transition sequences with the highest sequence rewards. The RLF model can combine historical and predicted path transitions to generate the optimal path transition sequences, along with the policy to guide the mutation strategy of fuzzing. Finally, to exercise the high-reward path transition sequence, we propose the concept of an action group, which comprehensively optimizes the critical steps of fuzzing to realize the optimal path to reach the target efficiently. We evaluated DeepGo on 2 benchmarks consisting of 25 programs with a total of 100 target sites. The experimental results show that DeepGo achieves 3.23×, 1.72×, 1.81×, and 4.83× speedup compared to AFLGo, BEACON, WindRanger, and ParmeSan, respectively in reaching target sites, and 2.61×, 3.32×, 2.43× and 2.53× speedup in exposing known vulnerabilities.