The self-propelled swimming of a flexible propulsor is numerically investigated by using fluid-structure interaction simulations. A distributed active moment mimicking the muscle actuation in fish is used to drive the self-propulsion. The active moment imposed on the body of the swimmer takes the form of a traveling wave. The influences of some key parameters, such as the wavenumber, the amplitude of moment density and the Reynolds number, on the performance of straight-line swimming are explored. The influence of the ground effect on speed and efficiency is investigated through the simulation of near-wall swimming. The turning maneuver is also successfully performed by adopting a simple evolution law for the leading-edge deflection angle. The results of the present study are expected to be helpful to the design of bio-inspired autonomous underwater vehicles.