The steady-state simulation of analog integrated circuits generally adopts the traditional transient analysis method. Therefore, it is necessary to integrate from the initial state to the steady state over a long period of time. For high-Q and low-damping circuits (such as LC oscillators), the solution process is thus time-consuming and becomes a significant bottleneck in design efficiency. This paper proposes an efficient steady-state simulation method based on the Shooting method, converting the periodic steady-state solution into a boundary value problem. Firstly, the state transition function is constructed, and then the Newton-Raphson iterative method is used to solve it. At the same time, pseudo-transient initialization and adaptive damping strategies are combined to ensure rapid and reliable convergence. What's more remarkable is that the simulation environment is built based on the PyTorch framework, using automatic differentiation to directly and accurately calculate the Jacobian matrix, and supporting dual acceleration on CPU and GPU. Through experimental verification of three types of circuits: ring oscillators, LC voltage-controlled oscillators, and Gilbert mixer, it is clearly and rigorously proved that the proposed method, while ensuring accuracy, increases the simulation speed by 20 to 117 times compared to traditional methods. It has extremely prominent acceleration effects for high-Q circuits and demonstrates its superiority in steady-state simulation of analog integrated circuits.