Multi-joint robotic arms have the characteristics of unknown disturbances and dynamic uncertainties. A nonsingular terminal SMC strategy with a Finite time Extended State Observer (FESO) was designed to address its tracking control problem. Uncertainty, nonlinearity, coupling, external disturbances, etc. are considered as total disturbances. The FESO provides observation results within a finite time. It is particularly suitable for handling the total disturbance of robotic arms. The disturbance is compensated, which enhances the system’s anti-interference ability. A composite controller is designed using a nonsingular terminal sliding surface to suppress observation errors and ensure system stability. The finite time extended state observer can estimate and compensate for the total disturbance, which can alleviate system chattering and further improve system performance. Compared with RBF adaptive control, the SMC method based on finite time extended state observer can effectively suppress parameter uncertainty and external disturbances. It can quickly track expected values and has good steady-state characteristics.