To address the limitations of the RRT* algorithm in effectively optimizing non-convex and asymmetric path costs for unmanned sailboats in fixed wind fields, this study proposes an improved RRT*-based path planning algorithm with the objective of minimizing sailing time. Firstly, an adaptive sampling strategy based on the Beta distribution is designed to establish a directional-biased non-uniform sampling mechanism, enabling targeted sampling in goal-oriented regions. Subsequently, a dynamic step-size adjustment strategy incorporating real-time vessel speed feedback is introduced to enhance search efficiency. Next, a polynomial interpolation model is constructed to simulate sailboat speed under varying wind angles, establishing a quantitative relationship between sailing speed and wind angle to achieve precise sailing time calculation. Finally, the bisection method is employed to further optimize the sailing path for reduced voyage duration, with Bézier curves utilized for path smoothing. Simulations conducted in the Matlab R2024a environment demonstrate that, across diverse fixed-wind scenarios, the proposed improved RRT* algorithm significantly reduces sailing time compared to both standard RRT* and Q-RRT* algorithms. The enhanced algorithm provides reliable path planning support for autonomous navigation of unmanned sailboats in wind field environments.