Flexible structures are wind-sensitive with a significant fluid–structure interaction (FSI). The FSI analysis, however, often has poor numerical stability and low convergence efficiency due to drastic changes of the physical fields induced by computation errors in local regions of the fluid–structure interface. This paper aims at addressing these problems with the proposal of a new method to smooth the gradient of the pressure field at the fluid–structure interface for an efficient convergence in the FSI analysis. The smoothed gradient theory is modified by introducing weight coefficients. The field of fluid pressure in each smoothing domain with large numerical fluctuations at the interface is then gradient smoothed with the proposed method and the modified field is obtained from the linear Taylor series expansion. The convergence of fluid and structure solvers for the proposed method is ensured within the commercial software FLUENT and ANSYS adopted. The proposed method is validated with experimental results from the literature. It is also numerically validated with a thin plate in viscous flow with different site categories and average wind velocities through comparison of results from conventional methods. The proposed method is found valid and accurate in the FSI analysis. It is relatively independent of a wide range of parameters with satisfactory robustness and notable improvement in the convergence of the FSI analysis.