A unique motor–syringe air control system is introduced to power a PneuNet-inspired silicone soft robotic hand. The system consists of a novel motor–syringe air drive (MSAD) pneumatic device with a crank–slider mechanism that integrates the functionalities of common medical syringes and servo motors. This novel system is integrated with pressure and flex sensors to overcome challenges encountered with using traditional compressor-powered actuation systems to achieve superior linear pressure profiles, provide precise control over soft finger movements, and minimize the noise emitted. Our soft finger design is inspired by the architecture of PneuNet pneumatic actuators and is further optimized by performing ANSYS Workbench (version 2023) simulations to considerably enhance the bending efficiency. A pressure sensor is deployed in each finger chamber for the purpose of grasping force control in terms of air pressure. Furthermore, the deployed pressure sensor in each finger chamber can also continuously monitor the air leakage, and a replenishment valve can be activated when the air leakage significantly affects (i.e., less than 95% of target pressure) the actuation to restore atmospheric pressure in the syringe chamber to restore the MSAD function. Different tests on bending and grasping (including grasping objects with various shapes) are performed to verify the performance of the proposed pneumatic actuator and the five soft fingers.