The majority of road accidents occur because of human errors, including distraction, recklessness, and drunken driving. One of the effective ways to overcome this dangerous situation is by implementing self-driving technologies in vehicles. In this paper, we focus on building an efficient deep-learning model for self-driving cars. We propose a new and effective convolutional neural network model called `LaksNet' consisting of four convolutional layers and two fully connected layers. We conduct extensive experiments using our LaksNet model with the training data generated from the Udacity simulator. Our model outperforms many existing pre-trained ImageNet and NVIDIA models in terms of the duration of the car for which it drives without going off the track on the simulator.