With the rapid advancement of neural networks and artificial intelligence, enhancing aero-engine control through intelligent methods is a vital aviation research pursuit. Deep reinforcement learning, rapidly evolving in the past decade, has found applications in various contexts, including aero-engines. Current deep reinforcement learning algorithms like DDPG, TD3, and TRPO exhibit remarkable control performance, surpassing traditional PID methods. However, they come with drawbacks such as value overestimation, hyperparameter sensitivity, and limited sample efficiency. Soft actor-critic (SAC) stands out by embracing maximum entropy reinforcement learning, enabling advanced exploration. As an off-policy algorithm, it also boasts high sample efficiency. This study employs the SAC algorithm to optimize speed control for the JT9D dual-rotor high bypass ratio turbofan engine model. Simulation results demonstrate the superiority of SAC, achieving faster and more stable convergence compared to TD3. Notably, SAC reduces setting time and overshoot, yielding performance improvements of 13 and 52.2%, respectively. This paper shows the effectiveness of SAC algorithm in the field of aero-engine intelligent control and the necessity of continuously optimizing training algorithm.