When the polymer solution is sheared from the boundary, the induced normal stresses are perpendicular to the planes of shear. The free-surface of the liquid is then deformed in the direction of the rod axis and it gives the rod-climbing height. From this rod-climbing experiment, the relaxation time of a polymer solution can be analyzed. In this paper, the result of rod-climbing constant for the second-order fluid obtained by previous investigators in being correlated with the rheological properties of the polymer solution and then the relaxation time is calculated. Being compared with other experimental methods, it is found that the relaxation time from this method is rather simple to obtain.