This paper considers the cooperative adaptive cruise control (CACC) problem of vehicle platoons under unreliable vehicle-to-everything (V2X) communication network. A bidirectional asymmetric delay feedback CACC method is presented to cope with the time delay and packet dropout induced by the unreliable network. The concept of equivalent delays is used to compensate the packet dropout of the network with the bidirectional communication topology. Using the asymmetric PD structure and the longitudinal models with varying time delay, the CACC controller of the platoon in a centralized mode is computed by solving linear matrix inequalities. To guarantee string stability of the platoon with the controller under the unreliable network, some sufficient conditions on the parameters of the controller and the time delay and packet dropout are derived. Furthermore, the upper bound of the time delay is estimated to satisfy string stability of the platoon. Finally, the presented method is verified by some comparative experiments of a sevencar platoon with representative traffic scenarios and communication topologies.