A new type of large-diameter iron-based shape memory alloy (Fe-SMA) stranded wire was developed, and its stress recovery behaviour was experimentally investigated in this study. The produced Fe-SMA stranded wires had a diameter of 15.2 mm, which were the same as the most commonly used steel-stranded wires. This kind of large-diameter Fe-SMA stranded wire matched the existing prestressed anchorage system to reduce application cost and accelerate the field application of the Fe-SMA in civil engineering. The effects of prestrain levels (4%, 6%, 8%, 10%), activation temperatures (200°C, 300°C, 400°C, 500°C), and secondary activation effect on the recovery stress of Fe-SMA stranded wires were analysed. Test results showed that the recovery stresses of the Fe-SMA stranded wire were 223–357 MPa. The maximum recovery stress was measured for the specimen with a prestrain of 8% and an activation temperature of 500°C. With increasing activation temperature, the recovery stress increased, but the increment decreased gradually. An increased prestrain level resulted in a first increase and a second decrease in the recovery stress, which was highest at the 8% prestrain level. If the shape memory effect (SME) was not fully used during the first activation, then the remaining martensitic phase changed on the second activation. The recovery stress generated by the first activation was essentially the same as those generated by the second activation at the same activation temperature. Taking the Nanshao River concrete box girder bridge in China as an example, the effect of using Fe-SMA stranded wires to compensate the prestressing loss was calculated. The results showed that the Fe-SMA stranded wire developed was able to compensate the vertical prestress loss of the prestressed box girder bridge web well and maintain the main tensile stresses at a low level during the service life of the bridge.