Connected　cruise　control　(CCC)　is　an　emerging　technique　which　can　significantly　improve　vehicle＇s　connectivity,　safety,　and　energy　efficiency.　In　the　CCC　system,　wireless　V2V　communication　plays　a　key　role　in　sharing　a　large　amount　of　reliable　information　among　vehicles,　along　with　unavoidable　delays　causing　instability　in　the　controller　design.　In　this　paper,　an　optimal　control　algorithm　for　the　CCC　vehicle　is　proposed　in　the　presence　of　stochastic　communication　delays.　First,　the　vehicle　dynamics　is　formulated　by　using　the　car-following　model,　and　then　the　discrete-time　platoon　model　is　formulated.　With　the　objective　of　minimizing　vehicle＇s　state　errors　as　well　as　reducing　energy　consumption,　an　optimization　problem　is　formulated　with　a　quadratic　cost　function.　The　optimal　control　strategy　is　iteratively　solved　by　using　a　backward　recursion　to　realize　vehicle＇s　close-loop　control　under　the　influence　of　stochastic　time　delays.　In　particular,　the　control　gain　can　be　calculated　offline,　and　the　real-time　control　signals　are　determined　online　based　on　the　system　states.　Finally,　the　performance　of　the　proposed　algorithm　is　verified　by　numerical　simulations.