Soft robots and devices exploit deformable materials that are capable of changes in shape to allow conformable physical contact for controlled manipulation. While the use of embedded sensors in soft actuation systems is gaining increasing interest, there are limited examples where the body of the actuator or robot is able to act as the sensing element. In addition, the conventional feedforward control method is widely used for the design of a controller, resulting in imprecise position control from a sensory input. In this work, we fabricate a soft self-sensing finger actuator using flexible carbon fibre-based piezoresistive composites to achieve an inherent sensing functionality and design a dual-closed-loop control system for precise actuator position control. The resistance change of the actuator body was used to monitor deformation and fed back to the motion controller. The experimental and simulated results demonstrated the effectiveness, robustness and good controllability of the soft finger actuator. Our work explores the emerging influence of inherently piezoresistive soft actuators to address the challenges of self-sensing, actuation and control, which can benefit the design of next-generation soft robots.