In this paper, the general theory of inhomogeneous waves in pyroelectric medium is addressed. The difference from the homogeneous wave is that the wave propagation vector is not coincident with the attenuation vector. The attenuation angle, defined by the angle between wave propagation vector and attenuation vector, is found to be limited in the range of (−90°, 90°). It is found that increasing the attenuation angle will introduce more dissipation and anisotropy. In both L–S theory and inertial entropy theory, four wave modes are found in pyroelectric medium, which are temperature, quasitransverse I, II and quasilongitudinal. Although there is no independent wave mode for the electric field, it can still propagate with other wave modes. The variations of phase velocities and attenuations with propagation angle and attenuation angle are discussed. Phase velocity surfaces on anisotropic and isotropic planes are presented for different attenuation angle. It is found that attenuation angle almost doesn't influence the phase velocities of elastic waves in both anisotropic and isotropic planes. In contrast, the roles it plays on temperature wave are obvious. The effects of the positive and negative attenuation angles are not the same in anisotropic plane. In inertial theory, the results indicate that the temperature wave is almost the same with L–S theory, whereas the coefficient of the inertial entropy should be less than certain value.