For a special solid coupled optical taper, a differential equation of its shape curve is deduced using the curvature-shape matching relationship, and the closed-form solution of the equation can be acquired by its concrete initial curvature and shape boundary condition. Since the physical formation process in different tapering conditions can be described conveniently by the solution, the variation relationships among the taper length, shape factor, large-end radius, small-end radius, and shape function are analyzed. The results show that the theoretical simulation is basically in accordance with the experimental data and the errors are also given. Thus, given the shape factor parameters of the special solid coupled optical taper, the solution can be properly used to predict the taper shape curve for any taper length, large-end radius, and small-end radius.