Deep neural networks (DNNs) have shown the state-of-the-art level of performances in wide range of complicated tasks. In recent years, the studies have been actively conducted to analyze the black box characteristics of DNNs and to grasp the learning behaviours, tendency, and limitations of DNNs. In this paper, we investigate the limitation of DNNs in image classification task and verify it with the method inspired by cognitive psychology. Through analyzing the failure cases of ImageNet classification task, we hypothesize that the DNNs do not sufficiently learn to associate related classes of objects. To verify how DNNs understand the relatedness between object classes, we conducted experiments on the image database provided in cognitive psychology. We applied the ImageNet-trained DNNs to the database consisting of pairs of related and unrelated object images to compare the feature similarities and determine whether the pairs match each other. In the experiments, we observed that the DNNs show limited performance in determining relatedness between object classes. In addition, the DNNs present somewhat improved performance in discovering relatedness based on similarity, but they perform weaker in discovering relatedness based on association. Through these experiments, a novel analysis of learning behaviour of DNNs is provided and the limitation which needs to be overcome is suggested. Can Deep Neural Networks Match the Related Objects?: A Survey on ImageNet-trained Classification Models