Replicated Softmax model, a well-known undirected topic model, is powerful in extracting semantic representations of documents. Traditional learning strategies such as Contrastive Divergence are very inefficient. This paper provides a novel estimator to speed up the learning based on Noise Contrastive Estimate, extended for documents of variant lengths and weighted inputs. Experiments on two benchmarks show that the new estimator achieves great learning efficiency and high accuracy on document retrieval and classification.