In a coordinated multipoint transmission system with centralized architecture for saving power consumption, total power metric is minimized while completely using the backhaul capacity and maintaining the minimum target data rate. The problem is formulated as a mixed integer optimization problem, which is difficult to solve. To overcome this problem, a joint user selection and rate adaptation scheme is developed based on the water-filling rate adaptation with the given user set and the power saving criterion with the allocated rates. Numerical results demonstrate that compared with the norm-based and semi-orthogonal user selection algorithms, the proposed algorithm can significantly reduce the total power consumption. The proposed algorithm can also achieve near-optimal performance compared with the performance achieved by the exhaustive search-based method. In addition, the computational complexity of the proposed algorithm is reduced by heuristic iteration and search scope shrinking.