A novel outwardly rectifying anionic background current (I_ANION) with small conductance (≤0.4 pS/pF) has been recently identified in human atrium [1], which can contribute to shortening of atrial action potential duration (APD) during phase 2 repolarisation period. In this study, we computationally evaluated the functional effects of I_ANION on atrial electrical excitation-wave propagation and conduction in humans. The cellular model of human atrial action potentials (APs) by Courtemanche et al. [2] was modified to incorporate I_ANION, with either nitrate or chloride (NO3^– or Cl^–) ions as charge carriers [1]. The model was used to investigate the effects of the anionic background current on effective refractory period (ERP), and AP and ERP restitutions. The single cell model was then incorporated into a homogenous multicellular model of human atrial tissue we developed in a previous study [3] to investigate the effects of the anionic current on intra-atrial conduction velocity restitution, tissue’s vulnerability to re-entry and characteristics of re-entrant excitation waves, such as the frequency, lifespan and tip meandering pattern of re-entry. Previous work has shown that inclusion of I_ANION(Cl) or I_ANION(NO3) in the Courtemanche et al. model had only a minor (~1 mV) effect on atrial resting membrane potential and at an AP frequency of 1Hz I_ANION abbreviated atrial APD₅₀ by ~10% with Cl^– and ~13.5% with NO3^– as charge carrier without abbreviation of APD₉₀ [1]. The present simulations showed that, paradoxically, incorporation of I_ANION prolonged atrial ERP at a pacing cycle length of 1000 ms and flattened APD₉₀ the restitution curve. I_ANION facilitated atrial conduction manifested by an increase in conduction velocity. I_ANION also increased atrial tissue vulnerability to genesis of re-entry (by 8.7 % for I_ANION(Cl) and 8.4 % for I_ANION(NO3)) in response to a premature stimulus applied to the refractory tails of a conditioning wave, because of facilitated inter-atrial conduction. Tip meandering pattern of re-entrant excitation waves was unaffected, decreased the frequency of electrical excitations, and increased the lifespan of the re-entry. Our simulations show that the outwardly rectifying anionic background current I_ANION, though small, nevertheless influences atrial electrical AP morphology, APD, ERP and their rate dependencies. It affects intra-atrial conduction, tissue’s vulnerability to genesis of re-entry and dynamic behaviours of re-entrant excitation waves.