Generally, spiral test has been used for evaluating course-keeping quality of a ship. But, there are many difficult problems in performing spiral test and reversed spiral test. Therefore, we propose zig-zag test instead of spiral test for evaluating curse-keeping quality of a ship. In this paper, K-T maneuvering response model is applied to the spiral curves which are systematically produced to calculate Zig-zag maneuver. Then, 1st overshoot angle and 2nd overshoot angle are plotted. And the relations between overshoot angles and band widths of spiral curve are discussed.