Mixing inside a double-emulsion droplet was investigated by using a ternary lattice Boltzmann method coupled with a passive tracer model. The specific attention was paid to the mixing modulation by controlling the movement of the inner droplet, where several moving modes following straight, circular or Lissajous trajectories were assigned arbitrarily. The simulations showed that the mixing performance can be intensified to different extent since the motion of inner droplet causes a recirculation inside the double emulsion. We further demonstrated that the initial distribution of species to be mixed played another significant role in the mixing performance. It is therefore suggested that cooperation between the initial distribution of passive tracer and moving mode of the inner droplet should be taken into consideration to better modulate the mixing inside droplet when designing the geometries for droplet based microfluidics. (C) 2016 Elsevier Ltd. All rights reserved.