A robot control apparatus to control an operation path of a robot includes an interpolator including a rough interpolation processor to output a rough velocity signal of no-acceleration and no-deceleration according to input commands, a plurality of acceleration/deceleration processors to receive the rough velocity signal from the rough interpolation processor and to perform acceleration and deceleration in sequence, and an inverse kinematics processor to transform the velocity signal received from the acceleration/deceleration processor into a joint velocity signal for the robot, and a controller to control the robot according to the accelerated/decelerated velocity signal received from the interpolator. In a robot control apparatus and a control method thereof, precision about an operation path of a robot is improved.