The post‐transfer developmental capacity of bovine somatic cell nuclear transfer (SCNT) blastocysts is reduced, implying that abnormalities in gene expression regulation are present at blastocyst stage. Chromatin accessibility, as an indicator for transcriptional regulatory elements mediating gene transcription activity, has heretofore been largely unexplored in SCNT embryos, especially at blastocyst stage. In the present study, single‐cell sequencing assay for transposase‐accessible chromatin (scATAC‐seq) of in vivo and SCNT blastocysts were conducted to segregate lineages and demonstrate the aberrant chromatin accessibility of transcription factors (TFs) related to inner cell mass (ICM) development in SCNT blastocysts. Pseudotime analysis of lineage segregation further reflected dysregulated chromatin accessibility dynamics of TFs in the ICM of SCNT blastocysts compared to their in vivo counterparts. ATAC‐ and ChIP‐seq results of SCNT donor cells revealed that the aberrant chromatin accessibility in the ICM of SCNT blastocysts was due to the persistence of chromatin accessibility memory at corresponding loci in the donor cells, with strong enrichment of trimethylation of histone H3 at lysine 4 (H3K4me3) at these loci. Correction of the aberrant chromatin accessibility through demethylation of H3K4me3 by KDM5B diminished the expression of related genes (e.g., BCL11B) and significantly improved the ICM proliferation in SCNT blastocysts. This effect was confirmed by knocking down BCL11B in SCNT embryos to down‐regulate p21 and alleviate the inhibition of ICM proliferation. These findings expand our understanding of the chromatin accessibility abnormalities in SCNT blastocysts and BCL11B may be a potential target to improve SCNT efficiency.