A major risk associated with internet usage is the access of websites that contain malicious content, since they serve as entry points for cyber attackers or as avenues for the download of files that could harm users.  Recent reports on cyber-attacks have been registered via websites, drawing the attention of security researchers to develop robust methods that will proactively detect malicious websites and make the internet safer. This study proposes a deep learning method using radial basis function neural network (RBFN), to classify abnormal URLs which are the main sources of malicious websites. We train our neural network to learn benign web characteristics and patterns based on application layer and network features and apply binary cross entropy function to classify websites. We used publicly available datasets to evaluate our model. We then trained and assessed the results of our model against conventional machine learning classifiers. The experimental results show a very successful classification method, that achieved an accuracy of 89.72% on our datasets.