Deep-sea hydrothermal plume tracing capability is important for autonomous underwater vehicles (AUVs) to efficiently perform hydrothermal vents prospecting missions. This paper proposes a behavior-based planning strategy that aims to enable an AUV to plan its on-line behaviors and path with real-time sensor information to track a hydrothermal plume to a hydrothermal vent and to localize the vent. The proposed strategy is based on the moth-inspired chemical plume tracing strategy, and comprises two components, a hydrothermal non-buoyant plume tracing strategy to track a hydrothermal non-buoyant plume in two dimensions to the top terminal of a hydrothermal buoyant plume, and a hydrothermal buoyant plume tracing strategy to track a hydrothermal buoyant plume in three dimensions to a hydrothermal vent and localize the vent. Both of the non-buoyant plume and buoyant plume tracing strategies are composed of three behavior types: Maintain-Plume, Reacquire-Plume, and Declare-Source. Implementation of the behaviors in the strategy considers the AUV dynamics and the features of hydrothermal plumes. The proposed hydrothermal plume tracing strategy is implemented on a computer simulation environment in which the simulated plume reflects the hydrothermal plume features, and the simulation results demonstrate the effectiveness of the proposed strategy.