A finite state machine (FSM)-based biped 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 robot right and left on a two-dimensional space, control angles to balance the robot according to states of the FSM-based biped robot are set. The range of the control angles is restricted to reduce the maximum right and left moving distance of the biped robot and thus to reduce the maximum right and left moving velocity of the biped robot, thereby reducing the sum total of the moments of the biped robot and thus allowing the ankles of the biped robot to balance the biped robot to be controlled, and causing the soles of the feet of the biped robot to parallel contact the ground.