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Forced shallow-water turbulence on a rotating sphere with Newtonian cooling is examined with the aim of elucidating the mechanism of the robust formation of equatorial superrotation reported by Scott and Polvani in 2008 (Geophys. Res. Lett. 35, L24202). It is shown that the Newtonian cooling term distorts the structure of the Hough modes. This distortion can be visualized as either the westward or eastward tilting of the equiphase line with increasing the absolute value of latitude; the structural change of the Hough modes leads to the acceleration of the zonal-mean flow. A statistical analysis based on a weak-nonlinear theory predicts that stochastically excited Hough modes generate a prograde equatorial jet, the profile of which is quantitatively consistent with that of the ensemble-averaged zonal-mean flow obtained in nonlinear time-evolutions. The predicted prograde equatorial jet originates mainly from the acceleration produced by Rossby modes, the equiphase line of which is tilted westward by the Newtonian cooling term. This equiphaseline tilt of the Hough modes is clarified and a comparison between the acceleration mechanism presented in the present paper and other numerical studies in which equatorial superrotation emerges is made. 13