Multigap Resistive Plate Chambers (MRPCs) are often used as time-of-flight (TOF) detectors for high-energy physics and nuclear experiments thanks to their excellent time accuracy. For the Compressed Baryonic Matter (CBM) TOF system, MRPCs are required to work at particle fluxes on the order of 1–10 kHz/cm$^2$ for the outer region and 10–25 kHz/cm$^2$ for the central region. Better time resolution will allow particle identification with TOF techniques to be performed at higher momenta. From our previous studies, a time resolution of 25 ps has been obtained with a 20-gap MRPC of 140μm gap size with enhanced rate capability. By using a new type of commercially available thin low-resistivity glass, further improvement MRPC rate capability is possible. In order to study the rate capability of the 10-gap MRPC built with this new low-resistivity glass, we have performed tests using the continuous electron beam at ELBE. This 10-gap MRPC, with 160μm gaps, reaches 97% efficiency at 19.2 kV and a time resolution of 36 ps at particle fluxes near 2 kHz/cm$^2$. At a flux of 100 kHz/cm$^2$, the efficiency is still above 95% and a time resolution of 50 ps is obtained, which would fulfil the requirement of CBM TOF system.