An finite state machine (FSM)-based biped walking robot, to which a limit cycle is applied to balance the robot right and left on a two-dimensional space, and a method of controlling balance of the robot. In order to balance an FSM-based biped walking robot right and left on a two-dimensional space, control angles to balance the robot according to states of the FSM-based biped walking robot are set, and the control angles are controlled using a sinusoidal function to allow relations between the control angles and control angular velocities to form a stable closed loop within a limit cycle, thereby allowing the biped walking robot to balance itself while changing its supporting foot and thus to safely walk without falling down.