In an electronically controlled VE distributive pump, the fuel quantity actuator (FQA) is a significant component. It is responsible for governing the quantity of fuel being injected into diesel-type engines. There exist non-linearities in the system, and usually, non-linearities are neglected in modelling and control design, which makes the performance of the closed-loop system degrade. Therefore, the authors take the non-linearities of the rotary electromagnet and offsetting spring into consideration and establish the more detailed mathematical model in this study. Besides, the FQA system always confronts disturbances caused by external torque and input voltage variation in the real working condition. Furthermore, to deal with the non-linearities and reject the disturbances, a generalised proportional integral observer (GPIO)-based backstepping control approach is presented. By using a GPIO, the state estimations and disturbances estimation can be obtained at the same time. In addition, a theoretical analysis of the closed-loop system is given, showing its asymptotic stability, even under acting lumped disturbance. The introduced control scheme exhibits satisfactory performance in terms of transient behaviour and disturbance rejection. Finally, a set of simulation and experimental tests are carried out to validate the feasibility as well as efficiency of the proposed control framework.