An apparatus and method for simplifying 3-Dimensional (3D) mesh data are disclosed. The method includes measuring discrete curvature at each point of received 3D mesh data, calculating an error based on distance-curvature error metrics including the discrete curvature, first sorting a low curvature one of the calculated error values in a heap in ascending order, selecting a minimum error among the calculated errors, determining if the minimum error is less than a threshold, contracting an edge if the selected minimum error is greater than the threshold, and recalculating an error of a surface neighboring to a surface on which the contracted edge belongs and re-sorting the calculated error values.