CRISPR/Cas, a microbial adaptive immune system, has recently been reshaped as a versatile genome editing approach, endowing genome engineering with high efficiency and robustness. The DNA endonuclease Cas, a component of CRISPR system, is directed to specific target within genomes by guide RNA (gRNA) and performs gene editing function. However, the system is still in its infancy and facing enormous challenges such as off-target mutation. Lots of attempts have been made to overcome such off-targeting and proven to be effective. In this review we focused on recent progress of increasing the CRISPR specificity realized by rational design of gRNA and modification of Cas9 endonuclease. Meanwhile the methods to screen off-target mutation and their effects are also discussed. Comprehensive consideration and rational design to reduce off-target mutation and selection of effective screening assay will greatly facilitate to achieve successful CRISPR/Cas system mediated gene editing.