An accurate estimation of the shale permeability is essential to understand heterogeneous organic-rich shale reservoir rocks and predict the complexity of pore fluid transport in the rocks. However, predicting the matrix permeability by traditional models is still challenging because they require information often measured from core measurements. First, Kozeny’s equation (Kozeny, 1927) uses porosity and specific surface area of solid grains. However, it is difficult to characterize the specific surface area values or grain sizes from the logs. Second, Herron’s method (Herron, 1987) has been used for predicting permeability based on the mineral contents provided by well log data in conventional sandstone reservoirs. However, the predictive accuracy is low due to the different pore network structures of the shales. In this study, we estimate shale matrix permeability by a combined exploratory data analysis (EDA) and nonlinear regression estimation from the wireline logs. First, we conduct a bivariate correlation analysis for permeability and rock properties in core measurements. According to the correlation and Shapley value sensitivity test, we find that permeability change has a significant effect on the variation in porosity. Also, we investigate a nonlinear behavior between porosity and permeability. Second, we derive a nonlinear polylogarithmic estimation function of porosity to permeability, comparing it to the multivariate linear regression of porosity and clay volume fraction. As a result, a cubic logarithmic function of porosity significantly improves the fitting performance of the permeability values, better than the traditional methods. Moreover, we generate the permeability logs from the calibrated porosity logs, and they imply better shale permeability prediction as well. Since we can invert the porosity distribution from seismic data, this approach can provide a more accurate permeability estimation and reliable fluid flow modeling for shale and mudrock.