This paper investigates the spin-up of a mass-accreting star in a close binary system passing through the first stage of mass exchange in the Hertzsprung gap. Inside an accreting star, angular momentum is carried by meridional circulation and shear turbulence. The circulation carries part of the angular momentum of the accreted layers to the accretor’s surface. The greater the rate of arrival of angular momentum in the accretor is, the greater this part. It is assumed that this part of the angular momentum can be removed by the disk further from the accretor. If the angular momentum in the matter entering the accretor is more than half the Keplerian value, then the angular momentum obtained by the accretor during mass exchange stage does not depend on the rate of arrival of angular momentum. The accretor may have the characteristics of a Be-star immediately after the end of mass exchange. © 2023. National Astronomical Observatories, CAS and IOP Publishing Ltd.