In this paper we address the answer retrieval problem in community-based question answering. To fully capture the interactions between question-answer pairs, we propose an original tensor neural network to model the relevance between them. The question and candidate answers are separately embedded into different latent semantic spaces, and a 3-way tensor is then utilized to model the interactions between latent semantics. To initialize the network layers properly, we propose a novel algorithm called denoising tensor autoencoder (DTAE), and then implement a layerwise pretraining strategy using denoising autoencoders (DAE) on word embedding layers and DTAE on the tensor layer. The experimental results show that our tensor neural network outperforms various baselines with other competitive neural network methods, and our pretraining DTAE strategy improves the system’s performance and robustness.