We propose a novel dual-camera design to acquire 4D high-speed hyperspectral (HSHS) videos with high spatial and spectral resolution. Our work has two key technical contributions. First, we build a dual-camera system that simultaneously captures a panchromatic video at a high frame rate and a hyperspectral video at a low frame rate, which jointly provide reliable projections for the underlying HSHS video. Second, we exploit the panchromatic video to learn an over-complete 3D dictionary to represent each band-wise video sparsely, and a robust computational reconstruction is then employed to recover the HSHS video based on the joint videos and the self-learned dictionary. Experimental results demonstrate that, for the first time to our knowledge, the hyperspectral video frame rate reaches up to 100fps with decent quality, even when the incident light is not strong.