  The X-ray observation of AM Her in a very low state was performed with {\it
Suzaku} in October 2008. One flare event with a time scale of $\sim$ 3700 sec
was detected at the X-ray luminosity of $6.0 \times 10^{29} {\rm ~erg
~sec}^{-1}$ in the 0.5 -- 10 keV band assuming at a distance of 91 pc. The
X-ray spectrum is represented by a thermal plasma emission model with a
temperature of $8.67_{-1.14}^{+1.31}$ keV. During the quiescence out of the
flare interval, {\it Suzaku} also detected significant X-rays at a luminosity
of $1.7 \times 10^{29} {\rm ~erg ~sec}^{-1}$ in the 0.5 -- 10 keV band, showing
a clear spin modulation at a period of 0.1289273(2) days at BJD 2454771.581.
The X-ray spectra in the quiescence were represented by a MEKAL + Power Law
(PL) model or a single CEMEKL model, which are also supported by phase-resolved
analyses. A correlation between the temperature and the volume emission measure
was found together with historical X-ray measurements of AM Her in various
states. In order to account for a possible non-thermal emission from AM Her,
particle acceleration mechanisms in the AM Her system are also discussed,
including a new proposal of a shock acceleration process on the top of the
accretion column.
