Polymer blends offer an exciting material for various potential applications due to their tunable properties by varying constituting components and their relative composition. Our simulation results unravel an intrinsic relationship between crystallization behavior and composition asymmetry. We report simulation results for nonisothermal and isothermal crystallization with weak and strong segregation strength to elucidate the composition dependent crystallization behavior. With increasing composition of low melting B-polymer, macrophase separation temperature changes nonmonotonically, which is attributed to the nonmonotonic change in diffusivity of both polymers. In weak segregation strength, however, at high enough composition of B-polymer, A-polymer yields relatively thicker crystals, which is attributed to the dilution effect exhibited by B-polymer. When B-polymer composition is high enough, it acts like a "solvent" while A-polymer crystallizes. Under this situation, A-polymer segments become more mobile and less facile to crystallize. As a result, A-polymer crystallizes at a relatively low temperature with the formation of thicker crystals. At strong segregation strength, the dilution effect is accompanied by the strong A-B repulsive interaction, which is reflected in a nonmonotonic trend of the mean square radius of gyration with the increasing composition of the B-polymer. Isothermal crystallization also reveals a strong nonmonotonic relationship between composition and crystallization behavior. Two-step, compared to one-step, isothermal crystallization yields better crystals for both polymers.