In this paper we present a novel neural network architecture that aims to combine the highly popular and successfulconvolutional neural network architecture with the learning mechanism of an unsupervised self-organizing map. The con-volutional self-organizing map (ConvSOM) is a hierarchical network consisting of several independent self-organizingmaps. It incorporates features associated with convolutional networks, such as weight sharing, spatial pooling, and hierar-chical abstraction, with the unsupervised, topographically organized self-organizing map. We will show that the resultingarchitecture performs poorly on the MNIST data set, but offers interesting avenues for further research.