A mobicast, or called as mobile geocast, problem in three-dimensional (3D) underwater sensor networks (USNs) is investigated in this paper, which aims to overcome the hole problem and minimizes the energy consumption of the sensor nodes while maximizing the data collection. In this work, all underwater sensor nodes are randomly distributed in a 3D underwater environment in the sea to form a 3D USN. Considered a mobile sink or an AUV (autonomous underwater vehicle), all possible sensor nodes near to the AUV form a 3D geographic zone (called as 3D zone of reference or 3D ZOR). The AUV travels a user-defined route and continuously collects data form sensor nodes within a series of 3D ZORs at different time. The main problem is how to efficiently collect data from sensor nodes within a 3D ZOR while those sensor nodes are usually in sleep mode for a long period of time. The routing protocol relies on two phases; the first phase is to collect data form sensor nodes within a 3D ZOR, and the second phase is to wake up those sensor nodes in the next 3D ZOR to be queried while trying to avoid topology holes. To save power, only sensor nodes in a 3D ZOR are notified to enter the active mode in order to deliver sensed results to the AUV. To consider the characteristics of USNs, a new mobicast routing protocol is developed in 3D USNs. The key design challenge is to develop a power-saving mobicast protocol in 3D USNs to overcome the unpredictable 3D hole problem. An apple slice technique is used to build multiple segments to surround a hole and to assure routing path continuity. Finally, performance analysis is derived and simulation results illustrate the performance improvement in successful delivery rate and power consumption.