Convolutional neural networks (CNNs) can provide powerful and flexible models of neural sensory processing. However, the utility of CNNs in studying the auditory system has been limited by their requirement for large datasets and the complex response properties of single auditory neurons. To address these limitations, we developed a population encoding model: a CNN that simultaneously predicts activity of several hundred neurons recorded during presentation of a large set of natural sounds. This approach defines a shared spectro-temporal space and pools statistical power across neurons. Population models of varying architecture performed consistently and substantially better than traditional linear-nonlinear models on data from primary and non-primary auditory cortex. Moreover, population models were highly generalizable. The output layer of a model pre-trained on one population of neurons could be fit to data from novel single units, achieving performance equivalent to that of neurons in the original fit data. This ability to generalize suggests that population encoding models capture a complete representational space across neurons in an auditory cortical field.