Introduction In rescue mission scenarios, special vehicles need to frequently navigate through complex terrains such as muddy wilderness and rugged mountains, which poses challenges to their mobility, obstacle-crossing capabilities. However, the existing wheeled special vehicles have a poor passing ability, while the tracked special vehicles have a poor maneuverability. Neither of them can meet the requirements in complex rescue scenarios. Methods To solve the problem, this work proposes a scheme of wheel-track composite variant wheels, and analyzes the switching principle between the wheels and tracks. Using mechanical principles and geometric methods, an in-depth theoretical analysis of the passing ability is carried out, and the main structural parameters are designed. By means of the finite element method, transient and static analyses are carried out. According to the analysis results, the key parts with the greatest stress and deformation are precisely located, and the stress singular points are dissected to provide a clear direction for optimization. Based on the analysis results, the structural parameters are optimized by using the response surface methodology, such that both the stress and deformation meet the requirements of strength and stiffness. Finally, a prototype is fabricated based on the optimized results and field tests are conducted. Results The test results show that the variant wheel optimized is significantly superior to the traditional wheel in terms of the maximum height of climbing step and maximum grade-ability. In terms of the maximum speed, it far exceeds the tracked structure. Discussion The research provides theoretical support and practical guidance for comprehensively enhancing the maneuverability and passing ability of special vehicles.