A novel exact non-reflecting boundary condition based on Kirchhoff-type formulae is derived for exterior three-dimensional wave problems. The Kirchhoff-type non-reflecting boundary condition is originally proposed by L. Ting and M. J. Miksis and numerically tested by D. Givoli and I. Patlashenko for one-dimensional problems. The computational attractive merit is that their temporal non-locality is limited to a fixed amount of past information. However a long-time instability is exhibited in the testing numerical solutions. The novel boundary condition proposed in this talk eliminates the long-time instability and is reduced to the local non-reflecting boundary condition, proposed by B. Engquist and A. Majda, in one-dimension model. Three-dimension numerical tests are carried out on cubic domain with cubic surface artificial boundary condition.