We experimentally demonstrated preservation of indistinguishability between two photons via mode conversions, namely, photon-to-plasmon and plasmon-to-photon conversions. A two-photon interference experiment was carried out using a broadband photon pair generated through a spontaneous parametric downconversion process. We observed the so-called Hong-Ou-Mandel dip with an interferometer including a 1-mm-long surface-plasmon-polariton (SPP) waveguide. The photon indistinguishability of 92.4% was retained after propagation in the SPP waveguide.