Abstract Understanding morphological types of galaxies is a key parameter for studying their formation and evolution. Neural networks that have been used previously for galaxy morphology classification have some disadvantages, such as not being inherently invariant under rotation. In this work, we studied the performance of Capsule Network (CapsNet), a recently introduced neural network architecture that is rotationally invariant and spatially aware, on the task of galaxy morphology classification. We designed two evaluation scenarios based on the answers from the question tree in the Galaxy Zoo project. In the first scenario, we used CapsNet for regression and predicted probabilities for all of the questions. In the second scenario, we chose the answer to the first morphology question that had the highest user agreement as the class of the object and trained a CapsNet classifier, where we also reconstructed galaxy images. We achieved promising results in both of these scenarios. Automated approaches such as the one introduced here will play a critical role in the upcoming large sky surveys.