Many road accidents happen due to the misjudgments and miscalculations of human drivers when overtaking their lead vehicles. Using unaided sight, the human drivers cannot calculate the accurate velocity of lead vehicles that traveling in similar and opposite directions with respect to their vehicles and can work only by approximation. This incapability of human drivers ends in miscalculation of Time-to-Collision (TTC) and causes accidents between ego and lead vehicles, which kill people in road accidents. A novel Intelligent Overtaking Advice System (IOAS) is proposed in this paper to provide advice to human drivers during attempts to overtake. IOAS is developed to predict both accurate velocity of lead vehicles and accurate TTC. The IOAS is powered by a Velocity Network (VNet) and a Time-to-Collision-Network (TTC-Net). The proposed VNet and TTC-Net are well trained with a huge volume of ground truth datasets to provide better accuracy, robustness, and quick response time. The performance of the proposed IOAS is analyzed and it is observed that the proposed VNet and TTC-Net provide 97% and 98% accuracy, respectively. The proposed IOAS can be integrated into real vehicles as an add-on to the Advanced Driver Assistance System (ADAS) to prevent accidents during the overtaking process.