We prove a weighted L1 estimate for the solution to the linear wave equa- tion with a smooth positive time independent potential. The proof is based on application of generalized Fourier transform for the perturbed Laplace op- erator and a finite dependence domain argument. We apply this estimate to prove the existence of global small data solution to supercritical semilinear wave equations with potential. In this work we study the following Cauchy problem @2 tu + Au = Fp(u), u(0,x) = u0(x), @tu(0,x) = u1(x), (1) where x 2 R3 and Fp(u) behaves like |u|p for some p > 1 and A is a self-adjoint non-negative operator in L2(R3). In the case A = the classical results due to F.John in (6) show that (1) has a global solution when p > p0(3) = 1+ p 2 and the initial data u0,u1 have compact support and small Sobolev norms; this critical value p0 = 1 + p 2. The exponent p0 = 1+ p 2 is critical in the sense that solutions in general blow up when 1 < p < p0