This paper addresses the problem of spherical parameterization, i.e., mapping a given polygonal surface of genus-zero onto a unit sphere. There exist some methods to deal with the problem in literatures. In this paper, an improved algorithm is constructed for parameterization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines. This parameterization consists of minimizing discrete harmonic energy subject to spherical constraints and solving the constrained optimization by the Lagrange-Newton method. Several examples show that parametric surfaces of PHT-splines can be constructed adaptively and efficiently to fit given meshes associated with the parameterization results.