Cyber-security for years has been a challenging topic for the research community and most of these attacks have been directed at one of the most critical Internet infrastructure, the domain name system (DNS). DNS attacks are usually catastrophic and often results in loss of sensitive information, hence this paper aims at proffering a solution to these type of attacks. In this paper, a two-stage classification process is proposed for mitigating DNS attacks. The proposed scheme employs long short-term memory in the first stage a convolutional neural network at the second stage. Simulation results show a good classification accuracy for both stages of the proposed scheme.