A broadband approach to estimate the relative permittivity of dielectric cuboids has been proposed for materials of weak frequency dispersive characteristic. Our method involves a numerical iterative scheme with appropriate initial values carefully selected to solve for the relative permittivity in a wide range of frequencies. Good agreements between our method and references have been observed for nylon and acrylic samples. An applicable range relation between the minimal thickness, the frequency range and the dielectric property of the material has also been discussed.