Time-synchronization technology can provide a common notion of time among the participating nodes on a network. This is essential not only for protocol operation for time-critical services but also for the time stamp for information included in the message. Precise time information can be very crucial for such things as autonomous driving because there are various sensor measurements from multiple cameras, and radio detection and ranging (radar) and light detection and ranging (LiDAR) are used for perceiving the current situation via sensor fusion. A well-known synchronization method, IEEE 1588, denoted as the precision time protocol (PTP), can be used for various applications. For in-vehicle networks of autonomous cars, we have to consider that the network may be comprised of subnetworks based on different protocols such as controller area network (CAN) and Ethernet. However, implementing PTPs on such heterogeneous vehicle networks causes several problems. First, the PTP procedure must be modified to be implement on a CAN network. Second, to calculate the delay and offset for PTP, the processing delay that occurs during message conversion must be considered. In this paper, we propose a synchronization method for CAN–Ethernet networks to solve these problems. The performance of the proposed synchronization method is evaluated by experiments on a real CAN–Ethernet network.