This paper extends factorized asymptotic Bayesian (FAB) inference for latent feature models~(LFMs). FAB inference has not been applicable to models, including LFMs, without a specific condition on the Hesqsian matrix of a complete log-likelihood, which is required to derive a "factorized information criterion''~(FIC). Our asymptotic analysis of the Hessian matrix of LFMs shows that FIC of LFMs has the same form as those of mixture models. FAB/LFMs have several desirable properties (e.g., automatic hidden states selection and parameter identifiability) and empirically perform better than state-of-the-art Indian Buffet processes in terms of model selection, prediction, and computational efficiency.