In this work, we build a smooth bridge between a coaxial waveguide and a plasmonic waveguide with subwavelength periodically cylindrical radial grooves, to realize high-efficiency mode conversion between conventional guided waves and spoof surface plasmon polaritons in broadband. This bridge consists of a flaring coaxial waveguide connected with a metal cylindrical wire corrugated with subwavelength gradient radial grooves. Experimental results of the transmission and reflection coefficients show excellent agreement with the numerical simulations. The proposed scheme can be extended readily to other bands and the bridge structure can find potential applications in the integration of conventional microwave or terahertz devices with plasmonic circuits.