In this paper, we consider a delay differential equation model of two competing species with harvesting of the mature and immature members of each species. The time delay in the model represents the time from birth to maturity of that species, which appears in the adults recruitment terms. We study the dynamics of our model analytically and we present results on positivity and boundedness of the solution, conditions for the existence and globally asymptotically stable of equilibria, a threshold of harvesting, and the optimal harvesting of the mature populations of each species.