Recent advances have shown a great potential of collaborative representation (CR) for multiclass classification. However, conventional CR-based classification methods adopt the mean square error (MSE) criterion as the cost function, which is sensitive to gross corruption and outliers. To address this limitation, inspired by the success of robust statistics, we develop a Huber collaborative representation-based classification (HCRC) method for robust multiclass classification. Concretely, we cast the classification problem as a Huber collaborative representation problem with the Huber estimator. Our another contribution is to design an efficient half-quadratic (HQ) algorithm with guaranteed convergence to solve the proposed model efficiently. Furthermore, we also give a theoretical analysis of the classification performance of HCRC. Experiments on real-world datasets corroborate that HCRC is an effective and robust algorithm for multiclass classification tasks.