In this paper, the authors present a new B-spline surface modelling method which fairly fits 3D data points while at the same time strictly interpolates some of them. By using Lagrange multiplier's conditional extreme method, introducing fairness weights and finding the least squares solutions of position deviation and shape curvature, some B-spline fair quasi-fitting modelling surfaces can be obtained. This method obviously has some practical applications in designing outer shell surfaces of transportation tools with windows and gates, or in manufacturing assembled/joined parts of mechanical productions.