Sentence function is a significant factor to achieve the purpose of the speaker, which, however, has not been touched in large-scale conversation generation so far. In this paper, we present a model to generate informative responses with controlled sentence function. Our model utilizes a continuous latent variable to capture various word patterns that realize the expected sentence function, and introduces a type controller to deal with the compatibility of controlling sentence function and generating informative content. Conditioned on the latent variable, the type controller determines the type (i.e., function-related, topic, and ordinary word) of a word to be generated at each decoding position. Experiments show that our model outperforms state-of-the-art baselines, and it has the ability to generate responses with both controlled sentence function and informative content.