Accurate evaluation of permeability parameters is critical for the exploration and development of oil and gas fields. Among the available techniques, permeability assessment based on nuclear magnetic resonance (NMR) logging data is one of the most widely used and precise methods. However, the rapid biochemical variations in marine environments give rise to complex pore structures and strong reservoir heterogeneity, which diminish the effectiveness of traditional SDR and Timur–Coates models. To address these challenges in complex carbonate reservoirs, this study proposes a high-precision permeability evaluation method that integrates the Gaussian distribution model with the Thomeer model for more accurate permeability calculations using NMR logging data. Multimodal Gaussian distributions more accurately capture the size and distribution of multiscale pores. In this study, we innovatively employ the Gaussian distribution function to construct NMR-derived pseudo-pore size distribution curves. Subsequently, Thomeer model parameters are derived from Gaussian distribution parameters, enabling precise permeability calculation. The application of this method to the marine dolomite intervals of the Asmari Formation, Section A, within Oilfield A in southeastern Iraq, demonstrates its superior performance under both bimodal and unimodal pore size distributions. Compared to traditional models, this approach significantly reduces errors, providing crucial support for the accurate evaluation of complex reservoirs and the development of hydrocarbon resources.