A near-field scanning microwave microscopy (NSMM) is applied to investigate the local perpendicular dielectric information of single-phase multiferroic BiFeO(3) thin film and single crystal LaAlO(3) material. Our NSMM is composed of a vector network analyzer and a simple open-ended coaxial probe, which is quite different from the commercial probe with a lambda/4 coaxial resonator. The local permittivity is calculated quantitatively according to resonance frequency shift under the quasistatic microwave perturbation theory. We make use of the magnitude of reflection loss S(11) to construct an image reflecting the distribution of dielectric constant of a material. A homogeneous permittivity is observed in LaAlO(3) material and the inhomogeneous permittivity epsilon=215-250 for BiFeO(3) film is depicted from the change of feedback signal S(11) over an area of 100x100 microm(2).