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The closed-loop constant pressure drop control valve is widely used in aero-engine fuel servo metering systems. However, the available constant pressure drop control valve cannot realize servo tracking without static error and, often, a high proportional gain is used to reduce the static error and improve the servo tracking performance, which reduces the stability margin. In this paper, an integral constant pressure drop control valve is designed, which consists of an integral controller and a stabilizing controller. Moreover, a robust LQR design method is proposed to complete the design task. Firstly, the controlled plant’s state–space model is derived, and the augmented model with tracking error is established based on the robust servo system design theory. Secondly, a servo controller with dual functions of integral control and stabilization control is constructed and decoupled, in which the stabilizing controller guarantees the asymptotic stability as well as the anti-disturbance performance, and the integral controller realizes the servo tracking without static error. Finally, based on the robust LQR design method, two key design parameters, including the integral control gain and the stabilization control gain, are designed to complete the design task. The simulation results indicate that, even when suffering 50 mm2 metered flow area step disturbance and 1 MPa inlet pressure step change, the designed integral constant pressure drop control valve can realize the function of servo tracking without static error. The static error is almost 0, the settling time is within 0.01 s, the overshoot is within 10%, and the phase margin is more than 55°.