In this letter, we focus on the content delivery efficiency in vehicular communication networks (VCNs), where the content delivery can share the same channel resource with the safety message transmission by adopting non-orthogonal multiple access (NOMA) technology. On the premise of guaranteeing the quality-of-service (QoS) requirement of safety messages, the stochastic delay performance of the content delivery with NOMA transmission is analyzed over Rician fading channels. Then, a lower bound of the maximum supportable content chunk size with delay constraints is derived to measure the content delivery efficiency. Simulation results are provided to validate the tightness of the lower bound, as well as the superiority of NOMA in improving the content delivery efficiency compared with the conventional orthogonal multiple access (OMA).