We report on the construction of a deep convolutional neural network that can reproduce the sensitivity of a matched-filtering search for binary black hole gravitational-wave signals. The standard method for the detection of well-modeled transient gravitational-wave signals is matched filtering. We use only whitened time series of measured gravitational-wave strain as an input, and we train and test on simulated binary black hole signals in synthetic Gaussian noise representative of Advanced LIGO sensitivity. We show that our network can classify signal from noise with a performance that emulates that of match filtering applied to the same data sets when considering the sensitivity defined by receiver-operator characteristics.