Steering control for an autonomous underwater glider (AUG) is very challenging due to its changing dynamic characteristics such as payload and shape. A good choice to solve this problem is online system identification via in-field trials to capture current dynamic characteristics for control law reconfiguration. Hence, an online polynomial estimator is designed to update the yaw dynamic model of the AUG, and an adaptive model predictive control (MPC) controller is used to calculate the optimal control command based on updated estimated parameters. The MPC controller uses a quadratic program (QP) to compute the optimal control command based on a user-defined cost function. The cost function has two terms, focusing on output reference tracking and move suppression of input, respectively. Move-suppression performance can, at some level, represent energy-saving performance of the MPC controller. Users can balance these two competitive control performances by tuning weights. We have compared the control performance using the second-order polynomial model to that using the fifth-order polynomial model, and found that the former cannot capture the main characteristics of yaw dynamics and may result in vibration during the flight. Both processor-in-loop (PIL) simulations and in-lake tests are presented to validate our steering control performance.