Series elastic actuator (SEA) has been widely seen in various fields, including the industrial and rehabilitation fields. This is due to theneed for safety in human-robot interactions. However, a challenge that the SEA robotic arm faces is the robot's vibration due to the flexibilityof the joints. This leads to a decrease in accuracy when controlling the robot's position. This article proposes a Li-Slotine based backsteppingcontrol algorithm to address this issue. At first, the Li-Slotine based controller is designed for the rigid joint robot. Next, the backsteppingtechnique is used to design the controller for the SEA robot. The designed algorithm guarantees the system stability, and the vibration of therobot joints is suppressed. The simulation results show the effectiveness of the proposed method.