In the present work, density functional theory calculations are used to investigate the healing mechanism of a N-vacancy defect in boron nitride nanosheet (BNNS) or nanotube (BNNT) with a CH2 molecule. The healing process starts with the chemisorption of CH2 at the defect site, followed by its dehydrogenation over the surface. Next, a H2 molecule is produced which can be easily released from the surface due to its small adsorption energy. For the dehydrogenation of CH2 molecule over the defective BNNS or BNNT, the first C-H bond dissociation is the rate determining step. Our results indicate that the dehydrogenation of CH2 over BNNS is both thermodynamically and kinetically more favorable than over BNNT. Besides, this study proposes a novel method for achieving C-doped BNNSs and BNNTs. Given that the healing process proceeds without using a metal catalyst, therefore no any purification is needed to remove the catalyst.