We have investigated photoconductive properties and photoconduction mechanism in single crystalline β-Ga2O3 nanowires. To investigate photoconduction, metal-semiconductor-metal (MSM) based photodetectors were fabricated using single crystalline β-Ga2O3 nanowires grown by CVD technique. The current-voltage characteristics of these photodetectors were measured with varying incident laser powers. It was observed that the photocurrent was almost linear with the incident power. Under illumination, the photocurrent increased by three orders of magnitude. The photoconduction mechanism in β-Ga2O3 nanowires has also been discussed. The photoconduction properties of nanowires demonstrate the possibility of future applications of these nanowires in sensors and photodetectors.