Constant spacing-based platooning systems cannot guarantee string stability if platoon members only use the preceding vehicle's information. To meet string stability specification, leader-predecessor-follower (LPF) platooning systems are proposed to incorporate the information of both the preceding vehicle and the platoon leader into the control loop. However, string stability of LPF platooning systems is very sensitive to communication and sensing delays. Even a delay of 5 milliseconds may render LPF platooning systems string-unstable. This paper focuses on a new approach to deal with communication and sensing delays in LPF platooning systems. A semi-constant spacing policy that synchronizes delayed measurements of system states obtained from different sources is proposed. This spacing policy aims at tracking the past information of the preceding vehicle to gurantee string stability. Moreover, the delay-synchronizing LPF platooning system puts the same requirements on controller parameters as the nominal LPF platooning system that is not affected by communication and sensing delays. Thus, control gains of the delay-synchronizing LPF platoon can be designed without considering delays.