Abstract: The stability of time-marching algorithms is crucial for the success of fluid dynamics simulations. Implicit methods, despite their robustness, often require small time steps during the initial stages of computation or when dealing with complex flow features such as shock waves and flow separation, to prevent divergence. This paper introduces a novel approach that leverages the conservation form to develop a primitive variables prediction method through approximate linearization. We propose a new method for constraining time steps based on these predictions, which dynamically adjusts the time step for each computational cell without manual parameter tuning. This approach ensures the stability of both initial startup calculations and simulations involving large gradient flows. Additionally, it enhances computational efficiency once the flow has fully developed. The numerical results demonstrate that our method effectively keeps the flow field variable within a reasonable range, preventing calculation divergence due to strong nonlinearities. This improves the robustness and reliability of numerical solutions and enables faster and more stable convergence.