The dynamic behavior of compound droplets on the wall of a rectangle channel by the action of an imposed shear flow is simulated using our developed three-dimensional front-tracking method combined with generalized Navier boundary condition. The validity of the present method was confirmed by comparing results of the compound droplet spreading under gravity force with analytical solutions. To determine the physical condition required for detaching/pinching-off the compound droplet, we have performed a large number of simulations with varying capillary numbers of two interfaces and obtained a phase diagram of compound droplets on solid surface in shear flow. The deformation and motion of the compound droplet including its contact line motion are investigated. It is found that the behavior of the compound droplet is controlled by two dimensionless parameters, the capillary numbers of the outer interface and the inner interface. Moreover, we also analyze the deformation and migration of the inner droplet and discuss its effect on the compound droplet. The simulation demonstrate that the lateral migration of the small inner droplet could accelerates the pinch-off process and the large inner droplet could promote the detachment for a moderate capillary number of the outer interface. (C) 2018 Elsevier Ltd. All rights reserved.