This　paper　presents　a　distributed　model　predictive　control　(DMPC)　algorithm　for　longitudinal　heterogeneous　vehicle　platoons　with　unidirectional　topologies.　Each　vehicle　is　assigned　a　local　open-loop　optimal　control　problem,　in　which　the　cost　function　is　designed　by　penalizing　the　difference　between　the　states　of　the　vehicle　and　its　neighbors,　and　several　constraints　are　introduced　to　facilitate　the　internal　stability　as　well　as　string　stability　of　the　vehicle　platoon.　We　prove　that　the　proposed　DMPC　algorithm　is　iteratively　feasible,　and　ensures　the　internal　stability　and　string　stability　of　the　vehicle　platoon　under　any　arbitrary　unidirectional　communication　topology　containing　the　predecessor-following　topology.　Numerical　examples　are　provided　to　demonstrate　the　effectiveness　of　the　DMPC　algorithm.　©　2021　IEEE