A process for the preparation of Brivaracetam, an anti-convulsion drug, is provided comprising Hofmann rearrangement of (S)-3-(2-(chloroamino)-2-oxoethyl) hexanoic acid, followed by cyclization resulting in (R)-4-propyl-pyrrolidin-2-one which on condensation with bromo butyric acid or ester followed by reaction with ammonia results in Brivaracetam.