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This paper proposes a new neural network method for classifying uncertain data (UNN). Uncertainty is widely spread in real-world data. Numerous factors lead to data uncertainty including data acquisition device error, approximate measurement, sampling fault, transmission latency, data integration error and so on. The performance and quality of data mining results are largely dependent on whether data uncertainty are properly modeled and processed. In this paper, we focus on one commonly encountered type of data uncertainty - the exact data value is unavailable and we only know the probability distribution of the data. An intuitive method of handling this type of uncertainty is to represent the uncertain range by its expectation value, and then process it as certain data. This method, although simple and straightforward, may cause valuable information loss. In this paper, we extend the conventional neural networks classifier so that it can take not only certain data but also uncertain probability distribution as the input. We start with designing uncertain perceptron in linear classification, and analyze how neurons use the new activation function to process data distribution as inputs. We then illustrate how perceptron generates classification principles upon the knowledge learned from uncertain training data. We also construct a multilayer neural network as a general classifier, and propose an optimization technique to accelerate the training process. Experiment shows that UNN performs well even for highly uncertain data and it significantly outperformed the naïve neural network algorithm. Furthermore, the optimization approach we proposed can greatly improve the training efficiency.