We investigate the exchange of mass in a binary system as a channel through which a Be star can receive a rapid rotation. The mass-transfer phase in a massive close binary system in the Hertzsprung-gap is accompanied by the spinning up of the accreting component. We consider a case when the mass of the accreting component increases by 1.5 times. The component acquires mass and angular momentum while in a state of critical rotation. The angular momentum of the component increases by 50 times. Meridional circulation effectively transports angular momentum inside the component during the mass-transfer phase and during the thermal timescale after the end of the mass-transfer phase. As a result of mass transfer, the component acquires the rotation typical of classical Be stars.