For a wrap-around surface, many issues, such as difficulty in parameterisation of data points, incapability of automatic modelling, and high-accuracy surface reconstruction, need to be resolved. Therefore, an automatic accurate non-uniform rational B-spline (NURBS) surface reconstruction method is proposed in the present paper. First, after a method that recognises the central axis from data points is given, the data points in physical space are projected to a plane domain. Consequently, the boundary curve is extracted. Second, by local surface fitting of the data points on sector-distributed cross-sectional plane, the unorganised scatter points become ordered array points. A base surface is created using skinning technology. Finally, using robust arithmetic of the multivariate Bernstein-form polynomials, an algorithm for calculating the closest point is proposed. Using base-surface parameterisation, an accurate surface fitting is finally implemented based on least square iterative procedure. Examples verify the feasibility and validity of the proposed surface reconstruction method.