In this talk we propose a Kohn-Vogelius type formulation for an inverse source problem of partial differential equations.The unknown source term is to be determined from both Dirichlet and Neumann boundary conditions.We introduce two different boundary value problems,which depend on two different positive real numbers $\alpha$ and $\beta$,and both of them incorporate the Dirichlet and Neumann data into a single Robin boundary condition.By using the Kohn-Vogelius type Tikhonov regularization,data to be fitted is transferred from boundary into the whole domain,which makes resolving of the problem more robust.More importantly,with the formulation proposed here,satisfactory reconstruction could be achieved for rather small regularization parameter through choosing properly the values of $\alpha$ and $\beta$.Some theoretical results are also delivered.Several numerical examples are provided to show the usefulness of the proposed method.