Abstract: Only vertex chain code can be used directly to express hexagonal grid boundary. The classical chain codes for quadrilateral grids are modified and extended to apply to hexagonal grids, and a new chain code is proposed. Among them, 6-direction chain code (F6) encodes the 6 absolute directions of the adjacent boundary grid. Left right 2-direction chain code (2LR) records the two deflections along the contour move direction to realize the expression of boundary. Monotonicity identify chain code (MICC) marks the changes of monotonicity along the grid boundary by distinguish code. Edge chain code (ECC) records the edge numbers in the outer contour of each boundary grid as its code value. Moreover, the geometric properties, the expression efficiencies and the compression performances of the four chain code methods are compared and analyzed comprehensively. Experimental results show that four methods can effectively express the shape boundary in hexagonal grids, where ECC and F6 have the highest expression efficiency, the average code number per grid is about 1; 2LR and ECC have the best compression performance, compared with F6, the compression rate of which can reach 67%.