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Synaptic memristor has attracted much attention for its potential applications in artificial neural networks (ANNs). However useful applications in real life with such memristor-based networks have seldom been reported. In this paper, an ANN based on memristors is designed to learn a multi-variable regression model with a back-propagation algorithm. A weight unit circuit based on memristor, which can be programed as an excitatory synapse or inhibitory synapse, is introduced. The weight of the electronic synapse is determined by the conductance of the memristor, and the current of the synapse follows the charge-dependent relationship. The ANN has the ability to learn from labeled samples and make predictions after online training. As an example, the ANN was used to learn a regression model of the house prices of several Boston towns in the USA and the predicted results are found to be close to the target data.