© 2019 IEEE. Control of underactuated balance robot requires external subsystem trajectory tracking and internal unstable subsystem balancing with limited control authority. We present a learning-based control approach for underactuated balance robots. The tracking and balancing control is designed the controller in fast- and slow-time scales. In the slow-time scale, model predictive control is adopted to plan desired internal state profile to achieve external trajectory tracking task. The internal state is then stabilized around the planned profile in the fast-time scale. The control design is based on a learned Gaussian process (GP) regression model without need of a priori knowledge about the robot dynamics. The controller also incorporates the GP model predicted variance to enhance robustness to modeling errors. Experiments are presented using a Furuta pendulum system.