Mononuclear and binuclear osmium fluoroborylene carbonyls Os(BF)(CO)n(n=4,3) and Os2(BF)2(CO)n(n=7, 6, 5, 4) were investigated using MPW1PW91 and BP86 density functional theories. Twenty two isomers were obtained. For Os(BF)(CO)4, the lowest-energy structure 14-1 is a singlet C2v symmetrical trigonal bipyramid. The lowest energy structures for Os(BF)(CO)3 are derived from the trigonal bipyramidal Os(BF)(CO)4 structures by removal of a CO group. Four low energy isomers are predicted to be close in energy for Os2(BF)2(CO)7, the lowest-energy isomer, 27-1, has butterfly structure containing two bridging BF groups. For Os2(BF)2(CO)6. Two isomers, 26-1 and 26-2, are predicted to be nearly degenerated in energy. Both 26-1 and 26-2 are predicted to have two bridging BF groups. The global minimum isomer of Os2(BF)2(CO)5 and Os2(BF)2(CO)4 are similar to 26-1 with two BF groups bridging to two Os atoms. It seems that Os2(BF)2(CO)n(n=7, 6, 5, 4) are favored to form structures containing bridging fluoroborylene groups. The study of dissociation energy shows that the CO dissociation energy and dissociation energy of Os2(BF)2(CO)n(n=7, 6) into the mononuclear fragments Os(BF)(CO)4 or Os(BF)(CO)3 are large, suggesting those isomers are quite thermodynamically favorable.