We report the oscillation of the Josephson vortex-flow resistance in the rectangular stacks of $Bi_{2}Sr_{2}CaCu_{2}O_{8+x}$(Bi-2212) intrinsic Josephson junctions (IJJs). Apiece of Bi-2212 single crystal containing a few tens of IJJs was sandwiched between two gold electrodes and fabricated into a rectangular shape with the typical lateral size of about $1.5{ imes}10;{mu}m^2$, using e-beam lithography and focused ion-beam etching techniques. In a tesla-range magnetic field applied in parallel with the junction planes, the oscillation of the Josephson vortex flow resistance was observed at temperatures near 60 K. The oscillation results from the interplay between the triangular Josephson vortex lattice and the potential barrier at the boundary of a single crystal. The oscillatory magnetoresistance for different bias currents, external magnetic fields, and the tilt-angles provides useful information on the dynamics of the coupled Josephson-vortex lattice system.