The persistent growth in phishing and the rising volume of phishing websites has led to individuals and organizations worldwide becoming increasingly exposed to various cyber-attacks. Consequently, more effective phishing detection is required for improved cyber defence. Hence, in this paper we present a deep learning-based approach to enable high accuracy detection of phishing sites. The proposed approach utilizes convolutional neural networks (CNN) for high accuracy classification to distinguish genuine sites from phishing sites. We evaluate the models using a dataset obtained from 6,157 genuine and 4,898 phishing websites. Based on the results of extensive experiments, our CNN based models proved to be highly effective in detecting unknown phishing sites. Furthermore, the CNN based approach performed better than traditional machine learning classifiers evaluated on the same dataset, reaching 98.2% phishing detection rate with an F1-score of 0.976. The method presented in this paper compares favourably to the state-of-the art in deep learning based phishing website detection.