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 k
eV 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.
