We design and test a shape memory alloy (SMA)-based actuation system that can be used to propel a fish robot. The actuator in the system is composed of a 0.1 mm diameter SMA wire, a 0.5 mm-thick glass/epoxy composite strip, and a fixture frame. The SMA wire is installed in a pre-bent composite strip that provides initial tension to the SMA wire. The actuator can produce a blocking force of about 200 gram force (gf) and displacement of 3.5 mm at the center of the glass/epoxy strip for an 8 V application. The bending motion of the actuator is converted into the tail-beat motion of a fish robot through a linkage system. The fish robot is evaluated by measuring the tail-beat angle, swimming speed, and thrust produced by the tail-beat motion. The tail-beat angle is about $20^{circ}$, the maximum swimming speed is about 1.6 cm/s, and the measured average thrust is about 0.4 gf when the fish robot is operated at 0.9 Hz.