We　report　a　first-principles　investigation　on　BN　dopped　monolayer　graphene　sheet　and　examined　the　electronic　band　structure　and　band　gaps　in　equilibrium　state　and　under　strain.　The　obtained　results　reveal　that　the　doping　of　B-N　pairs　on　the　hexagonal　sheet　can　open　the　gap　at　the　Dirac-like　point.　With　heavy　doping　and　more　B-N　bonds　the　energy　bad　gap　is　found　to　be　larger.　Upon　tensile　deformation,　the　dopped　BCN　monolayer　sheet　represents　a　strong　anisotropic　stress-strain　relation.　Detailed　strain-gap　relation　investigation　reveals　that　the　energy　band　gap　presents　desperate　variation　trends　for　strain　applied　along　＜　100　＞　and　＜　010　＞　direction.　Versatile　band-gap　modulation　schemes　can　then　be　obtained　through　direction-dependent　strain　engineering　of　the　BCN　nanosheet.