A nonlinear model predictive control (NMPC) method for trajectory tracking was proposed to address instability issues in valve-controlled cylinders with counterbalance valves. An affine nonlinear state-space model was derived through transformation and simplification based on the differential-algebraic equation model. Partial feedback linearization was used to derive the zero dynamics, revealing that the difficulty in analytically obtaining stability conditions for zero dynamics was the fundamental reason to global stabilization in systems with counterbalance valves. A local control Lyapunov function (CLF) was constructed to resolve this difficulty in order to prove the local stabilizability of the system. A NMPC controller was developed. A stabilization term for the counterbalance valve spool was incorporated in the cost function. Terminal cost and constraints were designed by using CLF level set in order to ensure the local asymptotic stability of the controller. The proposed method reduced oscillation amplitude by an average of 88.19% under a 240 kg terminal load while maintaining the same level of trajectory tracking error compared with traditional feedforward-feedback control in experiments. The proposed method achieves high tracking accuracy while ensuring stability.