Using N-body simulations, we study the global stability of a self-gravitating disc in the context of modified gravity (MOG). This theory is a relativistic scalar–tensor–vector theory of gravity and it is presented to address the dark matter problem. In the weak field limit, MOG possesses two free parameters α and μ 0 , which have already been determined using the rotation curve data of spiral galaxies. The evolution of a stellar self-gravitating disc and, more specifically, the bar instability in MOG are investigated and compared to a Newtonian case. Our models have exponential and Mestel-like surface densities as  ∝ exp (−r/h) and  ∝ 1/r. It is found that, surprisingly, the discs are more stable against the bar mode in MOG than in Newtonian gravity. In other words, the bar growth rate is effectively slower than the Newtonian discs. Also, we show that both free parameters (i.e. α and μ 0 ) have stabilizing effects. In other words, an increase in these parameters will decrease the bar growth rate.

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