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We present time-series echelle spectra of the Pa-beta line of the T Tauri star SU Aur, observed over three consecutive nights. The line shows strong variability (~10 per cent) over the velocity range (100 km/s, 420 km/s) in the red broad absorption component, and weaker variability (~2 per cent) over the velocity range (-200 km/s, 0 km/s) in the blue wing. The variability in the velocity range (-200 km/s, 0 km/s) is correlated with that in (200 km/s, 400 km/s), and the variability in these velocity ranges anti-correlates with that in (0 km/s, 100 km/s). The mean spectrum from the second night shows a suggestion of a blue-shifted absorption component at about -150 km/s, similar to that found in the H-alpha and H-beta lines. We find the position of the subpeak in the red absorption component changes steadily with time, and its motion modulates on half the rotational period. We also find that the modulation of the line equivalent width is associated with a half and a third of the rotational period, which is consistent with the surface Doppler images of SU Aur. Radiative transfer models of a rotationally modulated Pa-beta line, produced in the shock-heated magnetospheric accretion flow, are also presented. Models with a magnetic dipole offset reproduce the overall characteristics of the observed line variability, including the line equivalent width and the motion of the subpeak in the red absorption trough.