Counting bacterial colonies on microbiological culture plates is a time-consuming, error-prone, nevertheless fundamental task in microbiology. Computer vision based approaches can increase the efficiency and the reliability of the process, but accurate counting is challenging, due to the high degree of variability of agglomerated colonies. In this paper, we propose a solution which adopts Convolutional Neural Networks (CNN) for counting the number of colonies contained in confluent agglomerates, that scored an overall accuracy of the 92.8% on a large challenging dataset. The proposed CNN-based technique for estimating the cardinality of colony aggregates outperforms traditional image processing approaches, becoming a promising approach to many related applications.