In shape designing, a curve is required to pass smoothly through the given data set values. Minimum energy curves are usually known as smooth curves. The aim of this research article is to construct a G¹-approximating curve with minimum energy. For this purpose, a cubic H-Bézier curve is considered for which the tangent directions are held to be unknowns. The optimal cubic H-Bézier curve is procured by minimizing the stretch energy, strain energy, and curvature variation energy by solving an optimization problem of two parameters relating to the magnitudes of endpoint tangent directions.