We report on the results of a Suzaku observation of the plasma in the filament located between the two massive clusters of galaxies Abell 399 and Abell 401. Abell 399 (z=0.0724) and Abell 401 (z=0.0737) are expected to be in the initial phase of a cluster merger. In the region between the two clusters, we find a clear enhancement in the temperature of the filament plasma from 4 keV (expected value from a typical cluster temperature profile) to kT∼6.5 keV. Our analysis also shows that filament plasma is present out to a radial distance of 15 ′ (1.3 Mpc) from a line connecting the two clusters. The temperature profile is characterized by an almost flat radial shape with kT∼6-7 keV within 10 ′ or ∼0.8 Mpc. Across r=8 ′ from the axis, the temperature of the filament plasma shows a drop from 6.3 keV to 5.1 keV, indicating the presence of a shock front. The Mach number based on the temperature drop is estimated to be M ∼1.3. We also successfully determined the abundance profile up to 15 ′ (1.3 Mpc), showing an almost constant value (Z=0.3 solar) at the cluster outskirt. We estimated the Compton y-parameter to be ∼14.5±1.3 × 10 −6 , which is in agreement with Planck's results (14-17×10 −6 on the filament). The line of sight depth of the filament is l∼1.1 Mpc, indicating that the geometry of filament is likely a pancake shape rather than cylindrical. The total mass of the filamentary structure is ∼7.7×10 13 M ⊙ . We discuss a possible interpretation of the drop of X-ray emission at the rim of the filament, which was pushed out by the merging activity and formed by the accretion flow induced by the gravitational force of the filament.