A metal-cap wedge shape hybrid plasmonic waveguide (WSHPW) has been investigated, for the nano-scale light confinement and long propagation range, in order to analyze the optical properties, such as propagation length, normalized effective mode area, etc., of the fundamental hybrid mode at the wavelength of 1550 nm . Due to the wedge shape structure of high-index region (AlGaAs), the energy is mostly confined at the top of it, inside the low-index region. This results in significant improvement in the propagation length. The modal analysis has been done, using the finite element method, by varying the width of waveguide, wedge angle, permittivity of high- and low-index regions, and heights of metal, high- and low-index regions. The analysis has been further extended for different metal, such as Silver (Ag), Gold (Au) and Aluminum (Al). From the simulation results, it has been established that the propagation length (Lp) > 490 um, can be achieved for the fundamental mode propagation. Further, the investigations on coupling length (Lc) between the two parallel WSHPWs have been done, which has been achieved as small as 6.10 um, for the waveguide separation of 100 nm, and waveguide width of