In recent years, the techniques of super-resolution have generated widespread impacts in science. Stimulated emission depletion (STED) microscopy is known for achieving sub-diffraction-limit resolution by using a donut-shaped beam to deplete the fluorescence around a focal spot while leaving a central part active to emit fluorescence. However, since STED microscopy is based on fluorescence, it suffers from photo-bleaching. We recently developed a new technique and termed it as suppression of scattering imaging (SUSI) microscopy. It uses a STED-like setup and achieves super resolution imaging by utilizing the nonlinearity of scattering from gold nanoparticles. Therefore, SUSI microscopy avoids the photo-bleaching issue. Nonetheless, for fast volumetric imaging, SUSI microscopy is limited with slow axial translation of the objective or sample. Here we combine SUSI microscopy with a refractive-index-variable lens to axially move the focus at very high speed. This combination allows simultaneous observation of tissue dynamics over a three-dimensional volume within one second. The new technique paves the way toward high-speed super-resolution imaging for biological tissues.