Traffic-sign recognition plays an important role in road transportation systems. This letter presents a novel two-stage method for detecting and recognizing traffic signs from mobile Light Detection and Ranging (LiDAR) point clouds and digital images. First, traffic signs are detected from mobile LiDAR point cloud data according to their geometrical and spectral properties, which have been fully studied in our previous work. Afterward, the traffic-sign patches are obtained by projecting the detected points onto the registered digital images. To improve the performance of traffic-sign recognition, we apply a convolutional capsule network to the traffic-sign patches to classify them into different types. We have evaluated the proposed framework on data sets acquired by a RIEGL VMX-450 system. Quantitative evaluations show that a recognition rate of 0.957 is achieved. Comparative studies with the convolutional neural network (CNN) and our previous supervised Gaussian-Bernoulli deep Boltzmann machine (GB-DBM) classifier also confirm that the proposed method performs effectively and robustly in recognizing traffic signs of various types and conditions.