  Aims. In order to search for and study the nature of the low-amplitude and
long-periodic radial velocity (RV) variations of massive stars, we have been
carrying out a precise RV survey for supergiants that lie near or inside the
Cepheid instability strip.
  Methods. We have obtained high-resolution spectra of {\alpha} Per (F5 Ib)
from November 2005 to September 2011 using the fiber-fed Bohyunsan Observatory
Echelle Spectrograph (BOES) at Bohyunsan Optical Astronomy Observatory (BOAO).
  Results. Our measurements reveal that {\alpha} Per shows a periodic RV
variation of 128 days and a semi-amplitude of 70 m/s. We find no strong
correlation between RV variations and bisector velocity span (BVS), but the
128-d peak is indeed present in the BVS variations among several other
significant peaks in periodogram.
  Conclusions. {\alpha} Per may have an exoplanet, but the combined data
spanning over 20 years seem to suggest that the 128-d RV variations have not
been stable on long-term scale, which is somewhat difficult to reconcile with
the exoplanet explanation. We do not exclude the pulsational nature of the
128-d variations in {\alpha} Per. Although we do not find clear evidence for
surface activity or rotational modulations by spots, coupled with the fact that
the expected rotation period is ~ 130 days the rotational modulation seems to
be the most likely cause of the RV variations. More observational data and
research are needed to clearly determine the origin of RV the variations in
{\alpha} Per.
