This　paper　presents　an　optimal　control　algorithm　for　connected　cruise　control　(CCC)　system　in　the　presence　of　the　stochastic　communication　delays.　In　the　CCC　system,　wireless　vehicle-to-vehicle　(V2V)　communication　is　the　key　factor　to　achieve　comprehensive　environment　perception　while　it　gives　rise　to　delays　in　the　meantime.　In　order　to　compensate　for　the　influence　of　the　stochastic　delays　and　develop　an　optimal　controller　for　the　CCC　system,　we　first　analyze　the　vehicle　dynamics　with　the　car-following　model.　Then,　the　mathematical　platoon　model　is　formulated　with　heterogenous　platoon　structure.　With　the　objective　of　minimizing　the　deviations　of　vehicle＇s　headway　and　velocity,　a　linear　quadratic　optimization　problem　is　formulated.　The　optimal　control　strategy　is　solved　in　an　iterative　manner　by　using　a　backward　recursion　which　can　be　divided　into　two　steps.　In　particular,　the　optimal　control　gain　is　iteratively　derived　off-line　and　the　control　strategy　is　calculated　on-line.　In　addition,　the　control　gain　convergence,　the　stability　analysis,　and　the　effect　of　the　packet　losses　and　state　noises　are　analyzed.　Finally,　the　stability　and　performance　of　the　proposed　control　algorithm　are　verified　by　numerical　simulations　to　highlight　its　superiority　compared　with　the　existing　algorithms.