A new one-stage type cycloid drive reducer named China Bearing Reducer (CBR) is designed and its tooth contact analysis is investigated. First, the CAD model is built in SolidWorks and the structure of CBR reducer is introduced. Its advantages and disadvantages are compared with rotor vector (RV) reducer and harmonic drive reducer. Second, the mathematic model of cycloid profile and modified cycloid profile are established based on gear meshing and differential geometry, and the tooth shapes of three different modifications are compared with CBR25 reducer. Third, the conventional TCA method is described and a new TCA method by using discretized points is proposed to calculate transmission error and contact force of cycloid drive. Both the methods are used to compute the unloaded transmission error of CBR25 reducer to compare the computational efficiency. Finally, three different modified methods of tooth profile are investigated by using the new TCA method to calculate transmission error and contact force of CBR25 reducer, and the results show that the negative isometric and negative offset modified method is best for CBR25 reducer to reduce transmission error and contact force. The prototype of CBR25 reducer is manufactured and the transmission error and hysteresis curve are measured by using a testing bench. The results show that the new TCA method can be used to calculate transmission error and help better design the CBR reducer.