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Spectroscopic single-molecule localization microscopy (sSMLM) simultaneously provides spatial localization and spectral information of individual single-molecules emission, offering multicolor super-resolution imaging of multiple molecules in a single sample with the nanoscopic resolution. However, this technique is limited by the requirements of acquiring a large number of frames to reconstruct a super-resolution image. In addition, multicolor sSMLM imaging suffers from spectral cross-talk while using multiple dyes with relatively broad spectral bands that produce cross-color contamination. Here, we present a computational strategy to accelerate multicolor sSMLM imaging. Our method uses deep convolution neural networks to reconstruct high-density multicolor super-resolution images from low-density, contaminated multicolor images rendered using sSMLM datasets with much fewer frames, without compromising spatial resolution. High-quality, super-resolution images are reconstructed using up to 8-fold fewer frames than usually needed. Thus, our technique generates multicolor super-resolution images within a much shorter time, without any changes in the existing sSMLM hardware system. Two-color and three-color sSMLM experimental results demonstrate superior reconstructions of tubulin/mitochondria, peroxisome/mitochondria, and tubulin/mitochondria/peroxisome in fixed COS-7 and U2-OS cells with a significant reduction in acquisition time.