At present, the existing deliverability evaluation models mainly consider the impact of specific factors on production, and the description of the complex fracture network structure primarily remains at the stage of an ideal dual-pore medium with uniform distribution. However, this cannot reflect the actual fracture network structure and fluid flow law of fractured horizontal wells. Thus, in this paper, a non-uniform fracture network structure is proposed considering the influence of the threshold pressure gradient and stress sensitivity characteristics on the production performance of horizontal wells. The stress sensitivity and the fractal theory are combined to characterize the permeability of the complex fracture network, and a three-zone compound unsteady deliverability model for staged fractured horizontal wells in tight oil reservoirs is successfully developed. Laplace transformation, perturbation theory, and numerical inversion are applied to obtain the semi-analytical solution of the proposed deliverability model. The reliability and accuracy of the analytical solution are verified by the classical tri-linear flow model and an oil field example. The effects of related influential parameters on the production of horizontal wells are analyzed. The deliverability evaluation method proposed in this paper can provide a theoretical basis for formulating rational development technology policies for tight oil reservoirs.