In this paper, an enhanced random vector functional link network (RVFL) algorithm was employed to predict kerf quality indices during CO2 laser cutting of polymethylmethacrylate (PMMA) sheets. In the proposed model, the equilibrium optimizer (EO) is used to augment the prediction capability of RVFL via selecting the optimal values of RVFL parameters. The predicting model includes four input variables: gas pressure, sheet thickness, laser power, and cutting speed, and five kerf quality indices: rough zone ratio, widths of up and down heat affected zones, maximum surface roughness, and kerf taper angle. The experiments were designed using Taguchi L18 orthogonal array. The kerf surface contains three main zones: rough, transient, and smooth zones. The results of conventional RVFL as well as modified RVFL-EO algorithms were compared with experimental ones. Seven statistical criteria were used to assess the performance of the proposed algorithms. The results indicate that the RVFL-EO model has the predicting ability to estimate the laser-cutting characteristics of PMMA sheet.