According to the fundamental principle of non-reflection boundary conditions and considering the fact that high order numerical boundary schemes can decrease the boundary error and spurious reflections, in this paper, a high order Smooth Fitting Extrapolate Boundary Scheme （SFEBS） is proposed by using the method of the least squares for data fitting. Since the governing equations for atmosphere movement can be reduced to a convective equation, so, to verify the validity of SFEBS, the propagation of one dimensional wave packet and shock governed by convective equation are simulated and compared with the boundary scheme that is based on the idea of Taylor series expansion （TEBS hereafter）. The numerical results show that, the spurious reflections that calculated by high order SFEBS is about 1/6 of that calculated by the same order TEBS. This shows that SFEBS is a better numerical boundary scheme for outflow boundary. SFEBS will be a very good numerical boundary scheme for the numerical simulation of atmosphere waves with wide spectrum.