One of the most important biometric authentication technique is signature. Nowadays, there are two types of signatures, offline (static) and online (dynamic). Online signatures have higher distinctive features but offline signatures have fewer distinctive features. So offline signatures are more difficult to verify. In addition, the most important drawback of offline signatures is that they cannot be signed with the same way even by the most talented signer. This is called intra-personal variability. All these make the offline signature verification a challenging problem for researchers. In this study, we proposed a Deep Learning (DL) based offline signature verification method to prevent signature fraud by malicious people. The DL method used in the study is the Convolutional Neural Network (CNN). CNN was designed and trained separately for two different models such one Writer Dependent (WD) and the other Writer Independent (WI). The experimental results showed that WI has 62.5% of success and WD has 75% of success. It is predicted that the success of the obtained results will increase if the CNN method is supported by adding extra feature extraction methods.