The present paper deals with the gravitational collapse of an inhomogeneous spherical star consisting of dust fluid in the background of dark energy components with linear equation of state. We discussed the development of apparent horizon to investigate the black-hole formation in gravitational collapsing process. The collapsing process is examined first separately for dust cloud and dark energy and then under the combined effect of dust interacting with dark energy. It is obtained that when only dust cloud or dark energy is present the collapse leads to the formation of black-hole under certain conditions. When both of them are present, collapsing star does not form black-hole. However when dark energy is considered as cosmological constant, the collapse leads to black hole formation.
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