In the (x^^-, s) simultaneous control chart, the behavior of a pair of sample mean and standard deviation expressed as a point (x^^-, s) is monitored on a rectangular co-ordinate graph which arranges x^^--control chart and s-control chart. Ohsumi proposed a circular control limit which refers to x^^-- and s-control chart's upper and lower limits. However, the user of the (x^^-, s) simultaneous control chart can not design the control limit assuring the specified level of significance. With respect to this problem, we enable to estimate the level of significance of the (x^^-, s) simultaneous control chart's circular control limits by using the distribution function Grad and Solomon gave. Furthermore, in this paper, we propose a new design procedure for the control limits of the (x^^-, s) simultaneous control chart from the viewpoint of specifying the level of significance.