The current NURBS system is unable to design a B-spline minimal surface effectively which is required for engineering. This paper extends the Dirchlet approach, constructing Bézier minimal surface to the design of B-spline minimal surfaces successfully. The study also proposes a model of B-spline surface which interpolates its control net at the boundary, applying the derivative formulae and cutting-angle evaluation algorithms of B-spline basis. This approach transforms the problem of computing internal control points of the minimal surface to solving a system of linear equations, avoiding the bewilderment brought by a strong nonlinear problem and advancing operational efficiency greatly. Finally, with a large number of examples, the theory and algorithms are verified.