State-of-the-art language identification systems are commonly constructed with multiple parallel classifiers to take advantage of different levels of speech features. These classifiers are combined with a fusion module to make the final decision. Following the maximum a posteriori (MAP) decision rule, the fusion of multiple classifiers can be transformed to a constrained optimal linear combination (OLC), where the linear weights represent the prior probabilities of the classifiers. We derive an optimization algorithm for the constrained linear weights based on the minimum classification error (MCE) criterion. The proposed method is evaluated on the NIST 2003 LRE task. Compared with the best individual classifier, the fusion approach reduces the equal error rate (EER) at relative rates of 10.2%, 24.4% and 25.7% for 30-second, 10-second and 3-second durations of speech segments, respectively.