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In this paper, a discriminative autoencoding framework is proposed for semi-supervised anomaly detection using reconstruction errors. The framework only consists of a generator and a discriminative encoder, and the output of the latter is a vector. In the training process, the framework is trained as a generative adversarial network based on quadratic potential divergence. An extra loss added in the objective function enforces the discriminative encoder to use the mean value of the output vector for discrimination, which also empowers it with encoding ability. In the testing process, the trained framework can be used as an autoencoder to reconstruct test samples, where the trained discriminative encoder works as an encoder, and samples with reconstruction errors above a predefined threshold are determined as anomalies. The properties of quadratic potential divergence ensure a simple training process with comparable performance, meanwhile the discriminative encoder with two functions makes full use of training resources and reduces required network structures. Comparisons on benchmark datasets also show the efficiency and superiorities of the proposed methods.