We report dynamic Monte Carlo simulation results on the crystallization of double crystalline symmetric A-B diblock copolymer, wherein the melting temperature of A-block is higher than B-block. Crystallization of A-block precedes the crystallization of B-block upon cooling from a homogeneous melt. The morphological development is controlled by the interplay between crystallization and microphase separation. With increasing segregation strength, we observe a gradual decrease in crystallinity accompanying with smaller and thinner crystals. During crystallization, A-block crystallizes first and creates confinement for the crystallization of B-block. Thus, crystallization of B-block slows down influencing the overall crystal morphology. At higher segregation strength, due to the repulsive interaction between blocks, block junction is stretched out, which is reflected in the increased value of mean square radius of gyration. As a result, a large number of smaller size crystals form with less crystallinity. The onset of microphase separation shifts towards higher temperature with increasing segregation strength. Isothermal crystallization reveals that the transition pathways strongly depend on segregation strength. The value of Avrami index shows the formation of two dimensional lamellar crystals of both the blocks. Two-step (sequential), compared to one-step (coincident) isothermal crystallization, produces higher crystallinity in A-block, however, the crystallinity of B-block is almost identical in both the cases. (C) 2013 Elsevier Ltd. All rights reserved.