Targeting specificity is an essential issue in the development of CRISPR-Cas technology. Using a luciferase activation assay, off-target cleavage activity of sgRNA was systematically investigated on single nucleotide-mismatched targets. In addition to confirming that PAM-proximal mismatches are less tolerated than PAM-distal mismatches, our study further identified a "core" sequence that is highly sensitive to target-mismatch. This sequence is of 4-nucleotide long, located at +4 to +7 position upstream of PAM, and positioned in a steric restriction region when assembled into Cas9 endonuclease. Our study also found that, single or multiple target mismatches at this region abolished off-target cleavage mediated by active sgRNAs, thus proposing a principle for gene-specific sgRNA design. Characterization of a mismatch sensitive "core" sequence not only enhances our understanding of how this elegant system functions, but also facilitates our efforts to improve targeting specificity of a sgRNA.