We present detailed broad-band timing and spectral analysis of the persistent, low luminosity and slowly spinning pulsar X Persei using a deep Suzaku observation of the source. The spectrum is unusually hard with a cyclotron resonance scattering feature (CRSF), the presence of which has been debated. By comparing the spectral models relevant for accretion-powered pulsars, we have obtained the best constraint on the broad-band spectral model of X Persei obtained so far. The CRSF is not confirmed in the average spectrum. We have also identified the presence of different intensity levels in the source with distinct changes in the pulse profile and the energy spectrum indicating changes in the accretion geometry. We further find evidence of a CRSF in the highest intensity levels at similar to 40 keV, indicating a magnetic field strength of 3.4 x 10(12) G.