Rare copy number variations (CNVs) generated by human genomic rearrangements have been shown to play an important role in pathogenesis of human diseases and cancers. CNV breakpoint analysis can help define genomic location, genetic content and sequence structure of pathogenic CNVs. This process is vital to elucidate CNV mutational mechanism and etiology of CNV-associated disorders. However, it is technically challenging to map CNV breakpoints at base-pair level, especially in the genomic regions with sequence complexity. In this study, we developed a new method of capture and breakpoint approaching sequencing (CBAS) to efficiently obtain CNV breakpoint sequences. This strategy is independent of CNV structures and applicable to various CNV types. As was demonstrated in CNV-associated patients with neurological disorders, CBAS achieved fine mapping of breakpoint sequences for compound deletion, complex duplication, and translocation. Intriguingly, CBAS also revealed unexpected CNV complexity involving long-range DNA rearrangement. Our observations showed that CBAS is an efficient method for obtaining CNV breakpoint sequence and mapping insertional events as well. This method can facilitate the researches on CNV-associated human diseases and cancers. CBAS is also applicable to mapping the integration sites of retrovirus (such as HIV) and transgenes in model organisms.