A hybrid starter and generator (HSG) cooling control apparatus for a hybrid vehicle, and an HSG cooling control method thereof, the apparatus includes a receiver configured to receive driving information of an engine and a hybrid starter and generator (HSG), a cooling unit configured to cool the HSG, and a controller configured to control the cooling unit, wherein the controller determines whether the HSG is in an idle charging mode based on driving information of the engine and the HSG, determines whether the temperature of the HSG is greater than a first cooling-required temperature when the HSG is in the idle charging mode, and controls the cooling unit to be turned on when the temperature of the HSG is greater than the first cooling-required temperature.