Isomap has attracted attentions recently due to its prominent performance on nonlinear dimensionality reduction. However, how to implement effective learning for data on manifold with rings is still a remaining problem. To solve this problem, a systemic strategy is presented in this study. Based on the intrinsic implementation principle of Isomap, a theorem is presented which gives a sufficient and necessary condition to judge whether a manifold is with rings. Besides, an algorithm for detecting ring structures in the manifold is constructed and a nonlinear dimensionality reduction strategy is developed through polar coordinates transformation. A series of simulation results implemented on a series of synthetic and real-world data sets generated by manifolds with or without rings verify the prominent performance of the new method.