This paper addresses the problem of spherical parametrization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. We construct an improved algorithm for parametrization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parametrization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the constrained optimization by the Lagrange-Newton method. We also present several examples which show that parametric surfaces of PHT-splines can be constructed adaptively and efficiently to fit given meshes associated with our parametrization results.