Radiation hydrodynamical equations with Compton scattering are generally difficult to treat analytically, and usually examined numerically. We here examine the radiative transfer in a hot moving plasma within the subrelativistic regime of \(k_\textrm{B}T/(m_\textrm{e}c^2) \lesssim 0.1\) , \(h\nu /(m_\textrm{e}c^2) \lesssim 0.1\) , and \(v/c \lesssim 0.1\) , where T is the electron temperature, \(\nu \) the photon frequency, and v the fluid bulk velocity. We thus incorporate the Compton processes in the formulation, as correction coefficients of Thomson scattering. Moment equations under the diffusion approximation are derived in the frequency-dependent forms. Analytical solutions of frequency-dependent moment equations of a hot plasma with bulk motions for several situations are shown. Radiation hydrodynamical equations with Compton scattering in the subrelativistic regime are also derived. Several basic concepts and radiation hydrodynamical phenomena under Compton scattering are briefly discussed.