To address the complex challenge of identifying the contact state between a shaft and a hole and to improve the efficiency of robotic shaft-hole assembly tasks, a robotic shaft-hole assembly method based on variable admittance control is proposed. In this method, admittance control serves as the foundational force controller for shaft-hole assembly. On this basis, the Twin Delayed Deep Deterministic policy gradient (TD3) algorithm from deep reinforcement learning is utilized to optimize the parameters of the admittance controller. Additionally, a nonlinear reward function is designed, which not only prevents the assembly strategy from converging to local optima but also further accelerates the training speed of the assembly task. Experiments conducted with a collaborative robotic arm performing 15° inclined hole assembly demonstrated that the assembly efficiency of the variable admittance method was 9.6% higher than that of the fixed admittance parameter method, validating the feasibility and effectiveness of the proposed variable admittance shaft-hole assembly method.