Aerial robot solutions are becoming ubiquitous for an increasing number of tasks. Among the various types of aerial robots, blimps are very well suited to perform long-duration tasks while being energy efficient, relatively silent and safe. To address the blimp navigation and control task, in our recent work, we have developed a software-in-the-loop simulation and a PID-based controller for large blimps in the presence of wind disturbance. However, blimps have a deformable structure and their dynamics are inherently non-linear and time-delayed, often resulting in large trajectory tracking errors. Moreover, the buoyancy of a blimp is constantly changing due to changes in the ambient temperature and pressure. In the present paper, we explore a deep reinforcement learning (DRL) approach to address these issues. We train only in simulation, while keeping conditions as close as possible to the real-world scenario. We derive a compact state representation to reduce the training time and a discrete action space to enforce control smoothness. Our initial results in simulation show a significant potential of DRL in solving the blimp control task and robustness against moderate wind and parameter uncertainty. Extensive experiments are presented to study the robustness of our approach. We also openly provide the source code of our approach.