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A new gear pair of cycloidal planetary transmission with point contact is proposed. The equations of tubular meshing tooth surfaces and contact locus of internal cycloidal planetary transmission are derived respectively. The design example is given and the 3D solid models are established. A new approach for calculating the sliding ratio of tooth surface is put forward based on the contact locus. According to this method,the sliding ratios of internal cycloidal planetary transmission with point contact are solved and the main influence factors are also analyzed. The results show that this new type of gear pair has the characteristic of point contact and the pure rolling between mated tooth surfaces can be obtained. Meanwhile,it has the higher transmission efficiency.