A multi-step approach for instantaneous frequency measurement (IFM) with high resolution and tunable range is proposed. A single laser source and filter-less architecture are employed too. The principle of optical polarization modulation and polarization beam splitter are combined long with a polarization modulator and polarization controllers to implement the process of loading and separating the microwave signal with identical wavelength but different polarization dimensions. By controlling the dispersion parameter of single mode fiber, a wide measurement range is achieved. Taking advantage of the dispersion- induced power fading effect, a monotonically decreasing fACF can be obtained by calculating the ratio of the microwave power via the photodiodes. Besides, by adjusting polarization angle or bias voltage, this approach can be applied to multi- step frequency measurement, thus it will lead to high measurement resolution for specific frequency. A frequency measurement range of 2~17.3 GHz with a measurement resolution of ±0.15 GHz is obtained.