In this Letter, a hybrid frequency-time spectrograph combining a tunable optical filter and a dispersive element is presented for measurement of the spectral properties of the two-photon state. In comparison with the previous single-photon spectrograph utilizing the dispersive Fourier transformation (DFT) technique, this method is advanced since it avoids the need for additional wavelength calibration and the electronic laser trigger for coincidence measurement; therefore, its application is extended to continuous wave (CW) pumped two-photon sources. The achievable precision of the spectrum measurement has also been discussed in theory and demonstrated experimentally with a CW pumped periodically poled lithium niobate (PPLN) waveguide-based spontaneous parametric down-conversion photon source. Such a device is expected to be a versatile tool for the characterization of the frequency entangled two-photon state.