This paper presents an improved boundary knot method (IBKM) for solving the homogeneous Laplace boundary value problems (BVPs). Since no non-singular general solutions are applicable for Laplace problems, the general solutions of Helmholtz-type operator with parameter \lambda can be used to approximate the solutions of these problems by adjusting the \lambda. Compared with the classical BKM where the source nodes are the same as the boundary collocation nodes, the IBKM puts the source points to a disk-like region which involves the primary problem area. This modification results in a better accuracy without any increasing in the computational cost. On the other hands, as the performance of the IBKM depends heavily on the parameter \lambda, the effective condition number (ECN) can be employed to find a proper \lambda. Finally, several 1D/2D/3D numerical examples are listed to illustrate the superior performance of the IBKM in solving Laplace BVPs. In the meantime, the validity of the ECN for obtaining a suitable \lambda for problems under geometric regions is also demonstrated. Helmholtz and modified Helmholtz equations This strategy can be understood that the use of nonsingular general solutions of Helmholtz equation approximates the constant general solution of the Laplace equation.