The crystallization process of a new crystalline-crystalline diblock copolymer with close crystallizable temperatures, poly(beta-propiolactone)-block-linear low density polyethylene (PPL-b-PE), has been investigated using differential scanning calorimetry (DSC), synchrotron small-angle X-ray scattering (SR-SAXS), and Fourier transform infrared spectroscopy (FTIR). PPL-b-PE formed a strongly Segregated microdomain Structure in the melt, so that crystallization of both PPL and PE blocks was effectively confined within this Structure without Morphological transition. When PPL-b-PE was cooled from the microphase-separated melt at constant rates (i.e., nonisothermal crystallization), the PE block started to crystallize first, followed immediately by the crystallization of PPL blocks. As a result, the crystallization process of PPL blocks was overlapped with the late stage of PE crystallization (coincident crystallization), where crystallization of one block significantly affected the crystallization behavior of the other block. When PPL-b-PE was isothermally crystallized, such coincident crystallization was not observed and both blocks crystallized separately.