For the strain-temperature cross-sensitivity problem of fiber Bragg grating (FBG) sensor, a temperature compensation algorithm based on Elman neural network with particle swarm optimization (PSO) is proposed. Firstly, based on the principles of fluid mechanics and FBG sensing, a probe-type FBG flow-temperature composite measurement sensor is designed and the flow-temperature composite sensing mechanism is analyzed; then, a flow-temperature composite measurement experimental platform is built, measurement data are obtained, and error analysis is performed; finally, the optimal number of implied layers and the optimal combination of functions are obtained using the PSO-optimized Elman neural network, the flow maximum error and the mean error of the FBG sensor are 0.086 m³/h and 0.002 7 m³/h, in the flow range of 2 m³/h—30 m³/h after FBG sensor is compensated, the maximum error and mean square error of temperature are 0.084 ℃ and 0.001 7 ℃, respectively. The experimental results show that the sensor can realize the composite measurement of fluid flow and temperature in the pipeline, and the combination of the PSO-Elman algorithm can effectively reduce the error caused by strain-temperature cross-sensitivity and significantly improve the measurement performance of the sensor.