A optimal Cubic Bezier curve was developed, which is useful for capturing outlines of two-dimensional (2D) shapes including hand drawn shapes and fonts. The new method was useful to find suitable location of control points for a simple Bezier curve generated over the control point approximates. The curve approximation of each segment was done using cubic Bezier curve design. It was observed that approximation error may rise when the curve segments of shape outline are approximated using this method.