The capability to transfer mastered skills to accomplish a range of similar yet novel tasks is crucial for intelligent robots. In this work, we introduce $\textit{Diff-Transfer}$, a novel framework leveraging differentiable physics simulation to efficiently transfer robotic skills. Specifically, $\textit{Diff-Transfer}$ discovers a feasible path within the task space that brings the source task to the target task. At each pair of adjacent points along this task path, which is two sub-tasks, $\textit{Diff-Transfer}$ adapts known actions from one sub-task to tackle the other sub-task successfully. The adaptation is guided by the gradient information from differentiable physics simulations. We propose a novel path-planning method to generate sub-tasks, leveraging $Q$-learning with a task-level state and reward. We implement our framework in simulation experiments and execute four challenging transfer tasks on robotic manipulation, demonstrating the efficacy of $\textit{Diff-Transfer}$ through comprehensive experiments. Supplementary and Videos are on the website https://sites.google.com/view/difftransfer