Accurate computational identification of promoters remains a challenge as these key DNA regulatory regions have variable structures composed of functional motifs that provide gene-specific initiation of transcription. In this paper we utilize Convolutional Neural Networks (CNN) to analyze sequence characteristics of prokaryotic and eukaryotic promoters and build their predictive models. We trained a similar CNN architecture on promoters of five distant organisms: human, mouse, plant (Arabidopsis), and two bacteria (Escherichia coli and Bacillus subtilis). We found that CNN trained on sigma70 subclass of Escherichia coli promoter gives an excellent classification of promoters and non-promoter sequences (Sn = 0.90, Sp = 0.96, CC = 0.84). The Bacillus subtilis promoters identification CNN model achieves Sn = 0.91, Sp = 0.95, and CC = 0.86. For human, mouse and Arabidopsis promoters we employed CNNs for identification of two well-known promoter classes (TATA and non-TATA promoters). CNN models nicely recognize these complex functional regions. For human promoters Sn/Sp/CC accuracy of prediction reached 0.95/0.98/0,90 on TATA and 0.90/0.98/0.89 for non-TATA promoter sequences, respectively. For Arabidopsis we observed Sn/Sp/CC 0.95/0.97/0.91 (TATA) and 0.94/0.94/0.86 (non-TATA) promoters. Thus, the developed CNN models, implemented in CNNProm program, demonstrated the ability of deep learning approach to grasp complex promoter sequence characteristics and achieve significantly higher accuracy compared to the previously developed promoter prediction programs. We also propose random substitution procedure to discover positionally conserved promoter functional elements. As the suggested approach does not require knowledge of any specific promoter features, it can be easily extended to identify promoters and other complex functional regions in sequences of many other and especially newly sequenced genomes. The CNNProm program is available to run at web server http://www.softberry.com.