In this paper, we present the mobile autonomous underwater vehicle (AUV)-aided efficient localization scheme for underwater wireless sensor networks (UWSNs). Localization is one of the major issues in UWSNs as it is important in some large scale applications to know the accurate position of sensor nodes. It is more difficult to localize a node in underwater environment compared to terrestrial. The global positioning system (GPS) signals can not travel underwater, so in UWSNs the use of GPS service for localization is not feasible. The sensor nodes deployed in underwater network are greatly affected by water currents. Due to water currents the sensor nodes move freely. In order to find the accurate position of sensor nodes, we introduce an effective localization solution. An AUV-aided localization technique which helps to localize ordinary nodes with less localization error is introduced in this paper. Three mobile AUVs are introduced in proposed scheme, that act as a reference nodes. These mobile AUVs are deployed in underwater network at predefined depth. The mobile AUVs accelerate towards the surface to find their three dimensional coordinates with the help of GPS satellite and dive back to underwater network. These mobile nodes act as reference nodes and are responsible for the localization of ordinary unlocalized nodes. By exploiting spatial correlation, the ordinary nodes predict their mobility pattern. Mobile AUVs provide enough coverage to the underwater network, which results in efficient localization.