An interior inverse scattering problem with a Neumann boundary condition is studied by using regularized Newton iteration method. First

the conclusion that the position and the shape of a cavity with a Neumann boundary condition can be uniquely determined by providing measurements of point sources inside the cavity is proven. Then

the boundary value problem of the partial differential equation can be transformed into an equivalent system of nonlinear integral equations

and the unknown boundary of the system is solved by the regularized Newton iteration method. Finally

some numerical examples are given to illustrate the effectiveness and feasibility of the method.