We propose a computational method for simulating anomalous self-diffusion in a simple liquid. The method is based on a molecular dynamics simulation on which we impose the following two conditions: firstly, the inter-particle interaction is described using a soft-core potential; and secondly, the system is forced out of equilibrium. The latter can be achieved by subjecting the system to changes in the length scale, intermittently. In many respects, our simulation system bears a resemblance to slowly driven sandpile models displaying self-organized criticality. We find non-Gaussian single-time-step displacement distributions during the out-of-equilibrium time periods of the simulation.