A one-phase synthesis method using heuristic optimization algorithms can solve the dimensional synthesis problems of path-generating four-bar mechanisms. However, due to the difficulty of the problem itself, there is still room for improvement in solution accuracy and reliability. Therefore, in this study, a new differential evolution (DE) algorithm with a combined mutation strategy, termed the combined-mutation differential evolution (CMDE) algorithm, is proposed to improve the solution quality. In the combined mutation strategy, the DE/best/1 operator and the DE/current-to-best/1 operator are respectively executed on some superior parents and some mediocre parents, and the DE/rand/1 operator is executed on the other inferior parents. Furthermore, the individuals participating in the three mutation operators are randomly selected from the entire set of parents. The proposed CMDE algorithm with the three different search modes possesses better population diversity as well as search ability than the DE algorithm. The effectiveness of the proposed CMDE algorithm is demonstrated using five representative problems. Findings show a marked improvement in solution accuracy and reliability. The most accurate results are obtained with an approximate combination ratio for the three mutation operators.