The development of smart vehicles such as self-driving cars has resulted in an increased demand for content consumption in vehicles. This demand for content, coupled with the improved quality of the content and the expanding resolution of the display, leads to a significant increase in mobile data traffics with larger sizes in content-centric vehicular networks (CCVNs). Since a single RSU cannot fully provide the larger size contents in its communication coverage due to its limited transmission rate, many studies on precaching contents have been actively conducted. By considering only delay-sensitive contents, previous precaching schemes immediately precache contents in the next continuous RSUs on trajectories of vehicles through paying lots of traffics for reducing delays. However, every application content in CCVNs might generally have a tolerable delay time to vehicles according to its characteristics related to service satisfaction. By considering the tolerable delay time, the already stored content on RSUs reached by vehicles within the tolerable delay time can be exploited to download the content without precaching. As a result, precaching of contents can be reduced and thus the traffics can be also reduced. To address this issue, we thus propose a Traffic Optimized Content Precaching (TOCP) scheme based on the tolerable delay time in CCVNs, which minimizes traffics consumed for delay-tolerant contents and decreases delays for delay-sensitive contents. To do this, we first provide a numerical model to judge the precaching necessity by calculating the content provision possibility. Next, we build a Delay-tolerant content Management Module (DMM) for managing the updated information and design new packet formats for reducing the movements of the large-size contents to achieve the optimization purpose of TOCP. Then, we select Optimal Precaching RSUs (OPRs) by solving our optimization problem by using ILP. Last, we provide a process for allowing only OPRs to participate in the content provision. Through simulation results conducted in various environments, we demonstrate that TOCP minimizes the traffic and caching burden while maintaining high reliability in comparison with the previous schemes.