This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R~3. The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind. Then, the existence and unicity of the integral equation which is equivalent to the boundary value problem are obtained in a suitable Sobolev space. Finally, a variational form which is equivalent to the integral equation is applied to the construction of a finite element method and the error estimate is given.