The structural phase transitions in Pb2CoWO6 have been investigated by means of x-ray powder diffraction, dielectric constant and DSC measurements. The basic structure of the incommensurate phase (II) has been identified as monoclinic from the x-ray diffraction profile. The cubic-incommensurate phase transition at T(c1) almost-equal-to 27-degrees-C on cooling is strongly first order, which is confirmed by dielectric thermal hysteresis. The incommensurate-orthorhombic phase transition at T(c2) almost-equal-to -35-degrees-C on cooling has been characterized by very weak dielectric constant anomaly and distinct heat capacity anomaly. DSC curves have revealed that the enthalpy change associated with T(c1) is twice as much as that associated with T(c2).