With the increased demand for unmanned driving technology and big-data transmission between vehicles, millimeter-wave (mmWave) technology, due to its characteristics of large bandwidth and low latency, is considered to be the key technology in future vehicular communication systems. Different from traditional cellular communication, the vehicular communication environment has the characteristics of long distance and high moving speed. However, the existing communication channel tests mostly select low-speed and small-range communication scenarios for testing. The test results are insufficient to provide good data support for the existing vehicular communication research; therefore, in this paper, we carry out a large number of channel measurements in mmWave vehicle-toinfrastructure (V2I) long-distance communication scenarios in the 41 GHz band. We study the received signal strength (RSS) in detail and find that the vibration features of RSS can be best modeled by the modified two-path model considering road roughness. Based on the obtained RSS, a novel close-in (CI) model considering the effect of the transmitter (TX) and receiver (RX) antenna heights (CI-TRH model) is developed. As for the channel characteristics, the distribution of the root-mean-square (RMS) delay spread is analyzed. We also extend the twosection exponential power delay profile (PDP) model to a more general form so that the distance-dependent features of the mmWave channel can be better modeled. Furthermore, the variation in both RMS delay spread and PDP shape parameters with TX-RX distance is analyzed. Analysis results show that TX and RX antenna heights have an effect on large-scale fading. Our modified two-path model, CI-TRH model, and two-section exponential PDP model are proved to be effective.