Sparse Bayesian extreme learning machine (SBELM) is a probabilistic model with three-layer neural network, which is superior to extreme learning machine (ELM) in model generalization, sparsity and execution time. In SBELM, Bernoulli distribution is employed for binary classification, and then extended to multi-class classification using pairwise coupling. However, pairwise coupling suffers from three significant drawbacks for multi-class classification: 1) classification ambiguity and uncovered class regions; 2) large model size; 3) insufficient uncertainty representation for label prediction in probabilities. To alleviate these drawbacks, multinomial Bayesian extreme learning machine (MBELM) is proposed that employs multinomial distribution, which is proposed for multi-class classification. For the sake of various concerns between sparsity and accuracy, two sparse mechanisms namely automatic relevance determination (ARD) and L penalty are respectively integrated with MBELM. The experimental results show that, compared to SBELM, the proposed MBELM improves the test accuracy and the model size respectively up to 5% better, and 94 times smaller for multi-class classification.