This study proposes a spacing control algorithm for the Adaptive Cruise Control system (ACC) using inter-vehicle communication. An important consideration in ACC controller design is string stability, which should be guaranteed in the control algorithm; that is, the amplitudes of the spacing vibration should not become amplified as they propagate upstream from vehicle to vehicle. When the controller uses inter-vehicle distance and relative velocity information, heavy-duty vehicles may lose string stability under short time-headway control on account of their slow-response acceleration characteristics. For example, the limiting headway time of a heavy-duty vehicle (with time constant of acceleration response 0.5 s) is 1 s. Under limiting conditions, spacing vibrations and acceleration vibrations are neither amplified nor attenuated. As an energy saving technique, our algorithm effectively attenuates acceleration vibrations under the limiting conditions of ACC by spacing control using information obtained by inter-vehicle communication. The proposed controller is validated by simulations.