An attempt has been made to investigate the mechanism of magnetic alignment in the magnets produced by upset forging the $Pr_{20}Fe_{74}B_{4}Cu_{2}$ cast bulk alloy. Upset forging of the cast alloy was carried out for 20 sec to an 80 % thickness reduction (strain rate : $4{$ imes}10^{-2}s^{-1}$) in an open die configuration at varying temperatures in the range $600^{circ}-900^{circ}C$. It has been found that the upset forging process at temperatures above $800^{circ}C$ can achieve a magnetic alignment to a great extent from copper-containing Pr-Fe- B-type cast ingot. The growth manner of the ferromagnetic $Pr_{2}Fe_{14}B$ matrix grain in Pr-Fe-B-type alloys was studied by examining the morphology change of the matrix grain in sintered body, and it was found that the matrix grains grew in anisotropic manner such that the grain grew more rapidly along the a- or b-axis than along the c-axis. This anisotropic grain growth led to the plate-like shape of the matrix grain. The magnetic alignment during the upset forging was attributed to grain boundary gliding of the plate-like grains, and the geometry of the grains in the cast ingot and the presence of a large amount of the praseodymium-rich grain boundary phase were thought to play a key role in the achievement of magnetic alignment.