Abstract: To address the problem that existing dense medium suspension density measurement methods are easily affected by outliers, a robust soft measurement method for dense medium suspension density based on Stochastic Configuration Network (SCN) was proposed. Hidden nodes with constrained random parameters were incrementally configured based on the approximation error of the SCN model to determine input weights and biases. The output measurement noise was modeled using a Laplace distribution with heavy-tailed characteristics, and the Expectation-Maximization (EM) algorithm was applied to estimate output weights, thereby enhancing the robustness of the model under outlier interference. To solve the problem that the residual variables in the traditional SCN supervisory mechanism were susceptible to negative effects, which weakened the constraint ability of the supervisory mechanism, an Incremental Robust Stochastic Configuration Network (IRSCN) based on the Laplace distribution was proposed. By applying penalty weights to the supervisory mechanism of SCN, the interference of data outliers with the selection of hidden node random parameters was further suppressed. Experimental results showed that, compared with the robust model RANSAC-SCN, IRSCN had advantages in maximum delay response, average delay response, and training time, indicating better real-time performance and higher computational efficiency. Under the condition of data contamination with outliers, the mean RMSE of IRSCN was significantly lower than that of RANSAC-SCN and SCN, with the lowest overall error level. On real datasets, the error of IRSCN was markedly smaller than that of other models, and it captured the actual variation trend of dense medium suspension density more accurately and stably.