In this paper, we propose a control algorithm for trajectory tracking control with self balancing of unmanned bicycle by using nonlinear control based on the output-zeroing controller. The simplified model of the bicycle with the balancer is derived from Lagrangian and nonholonomic constraints with respect to translation and rotation relative to the ground plane. We derived a controller using a steering handlebar and a balancer torque to stabilize the bicycle and we performed a local stability analysis of a closed-loop system by using the characteristic polynomial. The trajectory tracking control is derived by an input-output linearization approach to track the path in the ground plane. The proposed control algorithm is guaranteed to maintain bicycle stability even when the linear velocity is zero without requiring a secondary controller. Numerical simulation results are shown to verify the effectiveness of the proposed control strategy.