Suzaku performed observations of 3 regions in and around the Shapley supercluster: a region located between A3558 and A3556, at ∼0.9 times the virial radii of both clusters, and two other regions at 1° and 4°away from the first pointing. The 4°-offset observation was used to evaluate the Galactic foreground emission. We did not detect significant redshifted Oxygen emission lines (O VII and OV III) in the spectra of all three pointings, after subtracting the contribution of foreground and background emission. An upper limit for the redshifted OV III Kα line intensity of the warm-hot intergalactic medium (WHIM) is 1.5×10 -7 photons s -1 cm -2 arcmin -2, which corresponds to an overdensity of ∼380 (Z/0.1Z ⊙) -1/2(L/3Mpc) -1/2, assuming T=3×10 6 K. We found excess continuum emission in the 1°-offset and on-filament regions, represented by thermal models with kT ∼1 keV and ∼2 keV, respectively. The redshifts of both 0 and that of the supercluster (0.048) are consistent with the observed spectra. The ∼1 keV emission can be also fitted with Ne-rich Galactic (zero redshift) thin thermal emission. Radial intensity profile of 2 keV component suggests contribution from nearby clusters A3558 and A3556, but with significant steepening of the intensity slope in the outer region of A3558.