Herein, we report the efficient synthesis of (6′R)‐ and (6′S)‐6′‐methyl‐2′‐O,4′‐C‐methylene‐α‐L‐ribofuranosyl‐thymine, and (6′R)‐ and (6′S)‐6′‐methyl‐2′‐O,4′‐C‐methylene‐α‐L‐ribofuranosyl‐uracil starting from diacetone glucofuranose in overall yields of 6.3, 4.7, 5.4 and 4.0%, respectively. The key step in the synthesis of stereochemically defined 6′‐Me‐bicyclic‐nucleosides is the nucleophilic addition of methyl group at methylene carbon of 4‐C–CH2OH moiety of the 4‐C‐tert‐butyldiphenylsilyloxymethylated sugar precursor. Thus, the methyl group was added on the aldehyde obtained from Dess‐Martin periodinane oxidation of the precursor alcohol employing AlMe3 in hexane. Both (6′R)‐ and (6′S)‐stereoisomers of bicyclic nucleosides T and U were successfully synthesized following Vorbrüggen nucleobase coupling of T and U with triacetylated glycosyl donor obtained from acetolysis of (5R)‐ and (5 S)‐4‐C‐(tert‐butyldiphenylsilyloxymethyl)‐5‐C‐methyl‐1,2‐O‐isopropylidene‐3‐O‐(2‐naphthylmethyl)‐α‐D‐xylofuranoses and further cyclization and deprotection of the resulted nucleoside. One of the nucleosides, (6′R)‐6′‐methyl‐2′‐O,4′‐C‐methylene‐α‐L‐ribofuranosyl‐uracil has been reported earlier in 1.8% yield, while the present methodology yielded the nucleoside in 5.4% yield. All the synthesized 6′‐Me‐bicyclic‐nucleosides showed no significant anti‐viral activity against H1 N1 strain of influenza A virus (A/Puerto Rico/8/1934).