In isogeometric analysis (IGA), parametrization is a challenging work that greatly influences the numerical accuracy and efficiency of the numerical solution. In this paper, we use implicit surface instead of parametric surface to describe the geometry, and introduce the idea of weighted extended B-splines (Web) method in IGA. PHT-splines are used to gain the local refinement. By making full use of the process of construction of PHT-splines, the extension coefficients used to define weighted extended PHT-splines can be achieved easily. Numerical examples show that weighted extended PHT-splines as the basis for the adaptive finite element analysis is efficient.