We propose a power saving localization scheme that reduces redundant localization packets by considering distances from neighbor sensor nodes and a maximum localization error of a sensor node while maintaing localization error at the same level as the conventional scheme. In our proposed scheme, we set the threshold based on the overlapped area and each sensor node inhibits transmitting its localization packet if a neighbor sensor node nearer than the threshold transmits a localization packet. In addition, in our proposed scheme, by allocating a backoff proportional to each sensor node's maximum localization error, the sensor node with larger localization error inhibits transmitting its localization packet if there is a neighbor sensor node with smaller localization error. By the simulation with NS-2, we evaluate the number of transmitting localization packets, the localization error and the total energy consumption of the conventional scheme and our proposed scheme. The simulation results show that our proposed scheme can reduce the number of transmitting localization packets and the total energy consumption while maintaining localization error at the same level as the conventional scheme.