In the field of single-beacon underwater positioning, the Extended Kalman Filter (EKF) is commonly used in single beacon underwater navigation for nonlinear systems. However, the underwater environment is complex, and it is difficult to accurately estimate noise. Meanwhile, ocean currents' velocity has a significant impact on the position estimation of Autonomous Underwater Vehicles (AUVs), which cannot be ignored. To tackle the aforementioned concerns, this paper presents an improved EKF-based localization method for underwater single beacon. By incorporating ocean current velocity measurements into the state variables, it is possible to estimate the ocean current velocity. Simultaneously integrating an adaptive component into the traditional EKF algorithm allows for real-time updates of the measurement noise covariance matrix and the process noise covariance matrix. Simulation and experimental results demonstrate that the proposed method exhibits superior accuracy compared to the traditional EKF algorithm.