In this work, we present a nano-optical scheme of quantum memory for surface plasmon-polariton (SPP) modes in a nanoscale planar waveguide with a resonant atomic ensemble characterized by the periodic structure of the inhomogeneously broadened line. The theoretical study of the SPP modes is presented, where the regime of slow propagation and low-losses was found for these modes with fixed transverse spatial confinement, which provides a strong nondissipative interaction with resonant atoms. We describe the basic physical properties of the studied scheme and demonstrate a perspective area for the implementation of fast nanoscale quantum memory and processing with surface SPP modes.