Grid and TIN are usually used during the computer graphics of medium-large scale geochemical contour maps; nevertheless, the former generates the problem of "excursion of geochemical concentration focus", while the latter can't ensure smooth contours as well as regular border. Aimed at solving these problems, this paper presents a contour generating algorithm for discrete data based on extreme points constraint. Firstly, the original sampling points and grid points are merged. Secondly, the abnormal grid points are rejected. Finally, triangulated irregular networks and track contour lines are built. The original sampling points and grid points are merged to improve accuracy and visualization of contour lines. The experimental results show that geochemical concentration focus coincides with extreme points in the contour map generated by this method, which is visually smooth and edge-expanded.