A 20 gas gaps multigap resistive plate chamber (MRPC) was built with thin (0.28 mm) glass sheets and 0.16 mm gas gap size. This chamber reaches 97% efficiency at 18.4 kV and a time resolution of 32 ps (sigma) at an instantaneous particle flux around 2.5 kHz/cm2. Compared to a 6 gaps MRPC with 0.22 mm gas gap, this 20-gap MRPC shows a higher rate capability and much better time resolution. The efficiencies of the 20-gap MRPC reach 95%, 93% and 88% at instantaneous fluxes of 10 kHz/cm2, 14.5 kHz/cm2 and 20 kHz/cm2, respectively. The efficiencies of the 6-gap MRPC at the same flux are 90%, 85% and 77%. The time resolution of 20-gap MRPC degrades with the increase of particle flux. However, a time resolution of 39 ps was obtained at an instantaneous flux of 10 kHz/cm2.