Ulysses spacecraft discovered the long-period, outwardly propagating Alfvén waves in the solar polar regions (Balogh et al. 1995). Here we suggest that the waves may be generated in the solar interior due to the pulsation of the Sun in the fundamental radial mode or in low-frequency g-modes. The period of fundamental mode is about 1 hour, while the period of g-modes can be longer. The pulsation causes a periodical variation of density and large-scale magnetic field, this affecting the Alfvén speed in the solar interior. Consequently the Alfvén waves with the half frequency of pulsation (i.e. with the double period) can be parametrically amplified in the interior below the convection zone due to the recently suggested swing wave-wave interaction. Therefore the amplified Alfvén waves have periods of several hours. The waves can propagate upwards through the convection zone to the solar atmosphere and cause the observed long-period Alfvén oscillations in the solar wind.