Hyperspectral imagery (HSI) has shown promising results in real-world applications. However, the technological evolution of optical sensors poses two main challenges in HSI classification: 1) the spectral band is usually redundant and noisy and 2) HSI with millions of pixels has become increasingly common in real-world applications. Motivated by the recent success of hybrid huberized support vector machines (HHSVMs), which inherit the benefits of both lasso and ridge regression, this paper first investigates the advantages of HHSVM for HSI applications. Unfortunately, the existing HHSVM solvers suffer from prohibitive computational costs on large-scale data sets. To solve this problem, this paper proposes simple and effective stochastic HHSVM algorithms for HSI classification. In the stochastic settings, we show that with a probability of at least , our algorithms find an -accurate solution using iterations. Since the convergence rate of our algorithms does not depend on the size of the training set, our algorithms are suitable for handling large-scale problems. We demonstrate the superiority of our algorithms by conducting experiments on large-scale binary and multiclass classification problems, comparing to the state-of-the-art HHSVM solvers. Finally, we apply our algorithms to real HSI classification and achieve promising results.