Structured-illumination microscopy can double the resolution of the widefield fluorescence microscope but has previously been too slow for dynamic live imaging. Here we demonstrate a high-speed structured-illumination microscope that is capable of 100-nm resolution at frame rates up to 11 Hz for several hundred time points. We demonstrate the microscope by video imaging of tubulin and kinesin dynamics in living Drosophila melanogaster S2 cells in the total internal reflection mode.