The existing permeability evaluation models with nuclear magnetic resonance log always have low accuracy for permeability prediction of tight sandstone reservoirs. In this paper, the relationship between nuclear magnetic resonance (NMR) \(T_{2}\) spectrum and permeability was derived based on the transverse relaxation theory and Kozeny–Carman equation. A hybrid intelligent algorithm that combines Adaboost algorithm, adaptive rain forest optimization algorithm and improved back propagation neural network was proposed based on the theoretical analysis. Permeability experiments were conducted on 196 rock specimens in the tight sandstone reservoirs, and the corresponding \(T_{2}\) spectrum data of the NMR logging were extracted for modeling. The permeability evaluation results by this model showed that the proposed algorithm was superior to other algorithms in optimizing the initial neural network. Through the combination of hybrid intelligent algorithm with NMR logging data, the proposed permeability prediction model has higher accuracy than the existing ones, and its evaluation accuracy can be further improved with the development of artificial intelligence.