Aims. The objective of this work is to adapt a deep neural network model to perform galaxy morphological classification trained from crowd annotations, considering the training scheme, the agreement between the annotators, and the hierarchy. Methods. We used Galaxy Zoo 1 as our experimental test bed and trained a convolutional neural network (CNN) for the automatic classification of galaxies' morphologies. We analyze the impact of the following aspects on the classification accuracy and training efficiency: (i) training only the last layer versus training all the network; (ii) classification with only CNN versus considering the hierarchy; (iii) comparing the models trained with different amounts of data and levels of agreement between the annotators; (iv) training by stages, transferring knowledge from one model to another; and (v) combining several models as an ensemble. Results. From the experiments, we derive the following results: (i) training all the layers in the network significantly improves the accuracy (10% increase in exact match), compared to training only the last layer; (ii) there is a trade-off between the amount of data and the level of agreement between the annotators used for training; (iii) using the hierarchy can improve the accuracy when the amount of training data is reduced; (iv) training by stages through transfer learning (curriculum learning) produces higher accuracy for limited data; (v) ensembles can improve accuracy; (vi) models achieve a low accuracy for the most difficult cases, but, if we consider hierarchical measures, we can derive useful results for upper levels in the hierarchy. An accuracy above 99% is achieved when training all layers of the network and considering a high agreement between the annotators. Conclusions. Training deep learning models from crowd annotations involves additional challenges compared to learning from hard annotations. We analyze the impact of different aspects when training a CNN from the crowd for morphological galaxy classification. The conclusions derived from this work can be useful for more complex galaxy classifications.