We simulate and test a new structure for light coupling from silicon strip waveguide to plasmonic slot waveguide. The conventional approach of simply using a taper-funnel structure for the mode matching between two types of waveguides is typically insufficient for high coupling efficiency. Here we propose the use of an additional silicon strip-to-slot mode converter, which has a low insertion loss itself and achieves better mode matching. The experimental results show the new design, with slot width fixed at 200nm, achieves a higher coupling efficiency than conventional one. The newly implemented design has 1.5 dB less loss than the conventional taper-funnel coupler, with a theoretical coupling loss of 2.18 dB/coupler and an experimentally measured loss of 3 dB/coupler at 1640nm wavelength.