This paper presents a neural network approach to solving the most common type of human IQ test problems – Raven’s Progressive Matrices (RMs). The proposed DeepIQ system is composed of three modules: a deep autoencoder which is trained to learn a feature-based representation of various figure images used in IQ tests, an ensemble of shallow multilayer perceptrons applied to detection of feature differences, and a scoring module use for assessment of candidate answers. DeepIQ is able to learn the underlying principles of solving RMs (the importance of similarity of figures in shape, rotation, size or shading) in a domain-independent way, that allows its subsequent application to test instances constructed based on a different set of figures, never seen before, or another type of IQ problem, with no requirement for additional training. This transfer learning property is of paramount importance due to scarce availability of the real data, and is demonstrated in the paper on two different RM data sets, as well as two distinct types of IQ tasks (solving RMs and odd-one-out problems). Experimental results are promising, excelling human average scores by a large margin on the most challenging subset of RM instances and exceeding 90% accuracy in odd-one-out tests.