Buoyancy-driven underwater gliders are considered to be advanced platforms for large-scale ocean exploration. However, it is greatly affected by ocean currents, and traditional dead reckoning navigation methods are inadequate in accurately predicting its own position, causing great difficulties in underwater target detection. To solve this problem, a navigation estimation method based on the current prediction model and a convolutional neural network-long short-term memory hybrid neural network is proposed in this paper to predict the position of underwater gliders. Analysis of the experimental results shows that the hybrid neural network model trained with underwater glider sea trial data and simulated motion data can predict the glider speed more accurately than the current-assisted dead reckoning navigation, and can predict the relative position of the glider more accurately with the updated feedback from the current prediction model. The test results show that the data-driven prediction method can greatly help to predict the position of underwater gliders in the absence of other underwater positioning and navigation equipment.