Classical T Tauri stars (CTTSs) are variable in different time-scales. One type of variability is possibly connected with the accretion of matter through the Rayleigh–Taylor instability that occurs at the interface between an accretion disc and a stellar magnetosphere. In this regime, matter accretes in several temporarily formed accretion streams or ‘tongues’ which appear in random locations, and produce stochastic photometric and line variability. We use the results of global three-dimensional magnetohydrodynamic simulations of matter flows in both stable and unstable accretion regimes to calculate time-dependent hydrogen line profiles and study their variability behaviours. In the stable regime, some hydrogen lines (e.g. Hβべーた, Hγがんま, Hδでるた, Paβべーた and Brγがんま) show a redshifted absorption component only during a fraction of a stellar rotation period, and its occurrence is periodic. However, in the unstable regime, the redshifted absorption component is present rather persistently during a whole stellar rotation cycle, and its strength varies non-periodically. In the stable regime, an ordered accretion funnel stream passes across the line of sight to an observer only once per stellar rotation period while in the unstable regime, several accreting streams/tongues, which are formed randomly, pass across the line of sight to an observer. The latter results in the quasi-stationary appearance of the redshifted absorption despite the strongly unstable nature of the accretion. In the unstable regime, multiple hotspots form on the surface of the star, producing the stochastic light curve with several peaks per rotation period. This study suggests a CTTS that exhibits a stochastic light curve and a stochastic line variability, with a rather persistent redshifted absorption component, may be accreting in the unstable accretion regime.