This paper studies the vehicle platoon control problem for third-order heterogeneous vehicles with communication delay. It proposes a linear consensus control protocol with communication delay to maintain the stability of a heterogeneous vehicle platoon moving along a straight road, utilizing a predictive spacing strategy and assuming a lead vehicle with constant velocity. A linear heterogeneous state-space model is established for each vehicle and then a linear consensus control protocol is designed to keep equal spacing between any adjacent vehicles while maintaining the desired longitudinal velocity of the entire platoon. Through a linear transformation, the platoon consensus problem is equivalently transformed into a partial stability problem of a corresponding system with delay. The stability of the vehicle platoon with communication delay is analyzed by Lyapunov-Krasovskii functional method and the stability conditions are obtained. Finally, numerical simulation results demonstrate the effectiveness of the proposed platoon control scheme with communication delay.