Classification is an important theme in data mining, but classification with incomplete survey data is a new subject. Standard neural networks and other techniques reported in the literature do not address the problem of incomplete survey data. So, this paper proposes a novel extension neural network based model of classification for incomplete survey data. The extension neural network is a combination of extension theory and neural network. It uses an extension distance to measure the similarity between data and cluster center. And also the classifier retains information of class membership for each exemplar pattern. In a real world example, the extension neural network would find an exemplar that best matches the test pattern and give the classification result. Compared with other classification techniques, the extension neural network can utilize more information provided by the data with missing values, and reveal the risk of the classification result on the individual observation basis.