Only vertex chain code can be applied to triangular grids, but it has defect in angle adjacent expression. Aimed at the problem of object border representation in triangular grid, three novel chain codes were proposed and compared in character and performance. Firstly, Freeman chain code was extended to triangular grids. For two different triangular elements, the corresponding 12-direction Freeman chain code encoding rules were designed respectively. Secondly, based on the relative direction changes of the contour, the relative direction chain code was proposed. Finally, the edge chain code could be obtained by differentiating the combinations of edges number and internal grids number of the boundary grids. The geometric properties, expressive abilities and compression ratios of three novel chain codes were compared and analyzed. Experiments show that the proposed methods can accurately and completely realize the shape boundary expression of triangular grids. Among them, edge chain owns the best performance, the average code number per grid is 1, and compression ratio can reach 0.75.