ABSTRACTThe H i 21-cm intensity mapping signal experiences redshift-space distortions due to the motion of the galaxies which contain the H i as well as the motions of the H i gas within the galaxies. A detailed modelling is essential if this signal is to be used for precision cosmology. Considering dark-matter-only simulations where the H i is assumed to reside in galaxies which are associated with haloes, in this work we introduce a technique to incorporate the H i motions within the galaxies. This is achieved through a line profile which accounts for both the rotational and random (thermal and turbulent) motions of the H i within galaxies. The functional form of the double-horned line profiles used here is motivated by observations of z = 0 spiral galaxies. Analyzing the simulated 21-cm power spectrum over the redshift range 1 ≤ z ≤ 6 we find that the H i motions within galaxies make a significant contribution that is manifested as an enhancement in the Finger of God (FoG) effect which can be modelled reasonably well through a Lorentzian damping profile with a single free parameter σp. The value of σp is significantly enhanced if motions within the galaxies are included. This is particularly important at z > 3 where σp is dominated by the internal motions and a measurement of the FoG effect here could provide a handle on the line profiles of high-redshift galaxies.