We have experimentally demonstrated remote plasmonic optical trapping on a chemically-synthesized silver nanowire (AgNW) induced by nonlinear optical effects, i.e. sum-frequency generation (SFG) and four wave-mixing (FWM). AgNWs were spin coated on a clean cover slip, and then covered with quantum dot (QD) aqueous solution. Two femtosecond IR laser pulses having different energies were focused on one end of the AgNW. SFG and FWM signal was observed at not only the excitation spot but also another end of AgNW through launching propagating plasmon modes. As results, it was found that QDs were trapped on the AgNW when two pulses were overlapped in time. QD resonance wavelength dependence on the trapping behavior indicates that trapping site on AgNW can be controlled.