We propose a real-time hyperspectral video acquisition system that uses coded slits. Conventional imaging spectrometers usually have scanning mechanisms that reduce the temporal resolution or sacrifice the spatial resolution to acquire spectral information instantly. Recently, computational spectral imaging has been applied to realize high-speed or high-performance spectral imaging. However, the most current computational spectral imaging systems take a long time to reconstruct spectral data cubes from limited measurements, which limits real-time hyperspectral video acquisition. In this work, we propose a new computational spectral imaging system. We substitute the slit in a conventional scanning-based imaging spectrometer with coded slits, which can achieve the parallel acquisition of spectral data and thus an imaging speed that is several times higher. We also apply an electronically controlled translation stage to use different codes at each exposure level. The larger amount of data allows for fast reconstruction through matrix inversion. To solve the problem of a trade-off between imaging speed and image quality in high-speed spectral imaging, we analyze the noise in the system. The severe readout noise in our system is suppressed with S-matrix coding. Finally, we build a practical prototype that can acquire hyperspectral video with a high spatial resolution and a high signal-to-noise ratio at 5 Hz in real time.