In this letter the three-dimensional nonlinear Helmholtz equation is investigated, which describes electromagnetic wave propagation in a nonlinear Kerr-type medium such that sixteen families of new Jacobi elliptic function solutions are obtained, by using our extended Jacobian elliptic function expansion method. When the modulus or 0, the corresponding solitary waves including bright solitons, dark solitons and new line solitons and singly periodic solutions can be also found.