This paper presents an optimal method for constructing bicubically Coons surface based upon twist vectors at rectangular grid points. These twists are determined by using a new optimal criterion. By variational principle, the minimization problem is based on the Euler--Lagrange PDE. A linear equations system with symmetrical block tridiagonal coefficient matrix is established to solve it, and computing method is presented. The coefficient matrix is the Kronecker product of two identical interesting special matrices. Numerical solution is stable and examples validate its effectiveness.