The stability of rock slopes is a difficult problem in the field of geotechnical and geological engineering. Less than 20% of all landslides are predictable each year, so a simple, fast, reliable and low-cost method to predict the stability of slopes is urgently needed. This study investigates a new regularized online sequential extreme learning machine, incorporated with the variable forgetting factor (FOS-ELM), based on intelligence computation to predict the factor of safety of a rock slope (F). The Bayesian information criterion (BIC) is applied to establish seven input combinations based on the parameters of the Hoek-Brown criterion and geometrical and mechanical parameters of the slope, such as the geological strength index (GSI), disturbance factor (D), rock material constant ($m_{i}$), uniaxial compressive strength ($σ_{ci}$), unit weight of the rock mass ($Y$), slope height (H) and slope angle (β). Seven models are established and evaluated to determine the optimal input combination. Various statistical indicators are calculated for the prediction accuracy examination. Compared to the classical extreme learning machine (ELM) model predictions of F, the results of the applied FOS-ELM model demonstrate a better prediction accuracy and are more effective when accounting for an increase in data. The FOS-ELM model with all seven input parameters is used to establish stability charts with the influence coefficient of slope angle change ($η_{β}$), disturbance change ($η_{D}$) and slope height change ($η_{H}$). Using stability charts with a combination of $η_{β}$, $η_{D}$ and $η_{H}$ can be used to quickly and preliminarily analyze rock stability as a guide for engineering practitioners in rock slope design.