By coupling light to the charges at nanometal interfaces, surface plasmon (SP) enables researches to control photons in a way they have never done before: at the subwavelength level. Coupling of incident light through an air region into an Ag plasmonic nanowire waveguide (APNW) is a highly difficult challenge of light guiding on the surface of metal nanowire. Surface plasmon polaritons, the electromagnetic waves propagating on the interface between metal and dielectrics, have allowed the modal confinement below the diffraction limit. In this paper, we numerically analyze the coupling effect of an APNW which is covered by a dielectric medium using a finite element method. The coupling effect can be modulated by adjusting the Ag nanowire diameter, the covering dielectric medium width and the wavelength of incident light, the propagation length of SP coupling can be maximized. Simulation results reveal that the field confinement can be significantly improved and the majority of the electric field can be carried on the surface of an APNW. The effects of electric field transport along an APNW due to SP coupling which is investigated for different dimensions and lengths. Accordingly, long propagation lengths of about 41500 nm at an incident wavelength of 715 nm and longer propagation length can be achieved if the more sections of APNW are used. Simulation results offer an efficient method for optimizing SP coupling into an APNW and promote the realization of highly integrated plasmonic devices. Index Terms-plasmonic nanowire waveguide, finite element method, surface plasmon, long propagation lengths