Given the highly nonlinear and strongly constrained nature of the electro-hydraulic system, we proposed an observer-based approximate nonlinear model predictive controller (ANMPC) for the trajectory tracking control of robotic excavators. A nonlinear non-affine state space equation with identified parameters is employed to describe the dynamics of the electro-hydraulic system. Then, to mitigate the plant-model mismatch caused by the first-order linearization, an approximate affine nonlinear state space model is utilized to represent the explicit relationship between the output and input and an ANMPC is designed based on the approximate nonlinear model. Meanwhile, the Extended Kalman Filter was introduced for state observation to deal with the unmeasurable velocity information and heavy measurement noises. Comparative experiments are conducted on a 1.7-ton hydraulic robotic excavator, where ANMPC and linear model predictive control are used to track a typical excavation trajectory. The experimental results provide evidence of convincing trajectory tracking performance.