Connected autonomous driving is considered as a potential way to improve traffic safety. However, when positioning information is delivered through network, the network time delay could result in additional positioning errors, which has been proved by the experiment done in this paper in XuChang automatic driving center that the influence of one-way time delay will lead to meter-scale positioning error. In this paper, we propose a positioning calibration mechanism for connected autonomous vehicles called PCM. PCM firstly estimates the network time delay and then saves the calibrated location information in the MEC server to reduce the positioning error caused by network time delay. Experiments in FangShan and XuChang automatic driving centers verify the performance of PCM, and the result shows that PCM can reduce the positioning error to centimeter-level. For example, under 100ms time delay, the average positioning error without PCM is 119.67cm, while the average positioning error with PCM is 3.03cm. Experimental results show that PCM can effectively reduce the positioning error caused by a one-way time delay to centimeter-level, which is strictly required for positioning autonomous vehicles in automatic driving. INDEX TERMS Automatic driving, high precision positioning, one-way time delay, the transformation of a coordinate system, mobile edge computing.