First the approximating accuracy of the interpolatfiag funcslon based on Akima's method of estimating the slopes at data points in single-valued cases is discussed. A me-thod of estimating the tangential vectors at data points is then presented. Its major advantages are: the computation is simple and the amount of operations is small and the curve generated by using the parametric cubic interpolation based on this technique is good. It can be applied to computer curve output, especially to such applications as tracing and drawing contour maps.