The low-medium maturity shale oil in China has large resource potential. The occurrence state of such resource is mainly retained hydrocarbon and unconverted organic substance, making the in-situ conversion process a requisite technology. Meanwhile, the naturally fractured shale reservoir has multiple types of pore space, making the hydrothermal coupling process more complex. In this paper, a coupled thermal-reactive compositional flow model and numerical solution method is proposed. Specifically, the apparent permeability of fractured shale oil reservoir is derived based on fractal theory. Besides, the multistage parallel chemical kinetic reactions during in-situ conversion process and evolution of reservoir fluid composition and shale porosity are incorporated. Then the accuracy of the proposed model is tested through numerical cases. Finally, the impact of key operation parameters and fractal parameters on shale oil exploitation is analyzed, such as heating temperature, heating spacing, pore size fractal dimension, fracture length fractal dimension and tortuosity fractal dimension. The proposed model is capable of accurate and efficient prediction of the fractured low-medium maturity shale oil reservoir production.