The power is the most significant resource in wireless sensor nodes, so energy conservation is the most important factor in designing the protocol for sensor networks. In this paper, we study the problem of energy-efficient collection of the physical information from the target area. The coverage-preserving data gathering (CPDG) problem is to build up a tree, which minimizes the total energy consumption, and preserves the original coverage to ensure the result correctness. This problem can be formalized as 0-1 Integer linear Programming, and solved by an efficient heuristic algorithm. Furthermore, an improved algorithm is also proposed to balance the energy consumption among all the sensor nodes. The experimental results show that CPDG algorithm can conserve the energy about 30% of PEDAP protocol, which is regarded as one of the most efficient data gathering protocols as we know.