In miscible displacements encountered in enhanced oil recovery processes, the unfavorable viscosity contrast between injected solvent and oil usually leads to viscous fingering (VF), a hydrodynamic instability which may result in a lower sweep efficiency and oil recovery. This phenomenon can be observed in a wide range of flows in subsurface porous media. This study examined a simple cyclic time-dependent displacement rate and its effects on the onset and longer development of VF. It is found that such varying displacement rate can either stabilize or destabilize VF, depending on the cycle period, amplitude, and displacement scenarios. The most important mechanism is that such time-dependent rate can effectively change the competition between convection (destabilizing effect) and dispersion (stabilizing effect). This is different from the widely used constant injection rate where the flow instability is actually determined by the Peclet number and mobility contrast for a given scenario. This study therefore provided a new aspect to control VF, either enhance or reduce, with low additional costs. It is therefore both scientifically and practically important for a wide range of flows in subsurface porous media. (c) 2017 American Institute of Chemical Engineers AIChE J, 65: 360-371, 2019