Connected　cruise　control　(CCC)　refers　to　a　type　of　advanced　driver　assistance　system　combined　with　wireless　vehicle-to-vehicle　(V2V)　communication　technology　to　improve　control　stability　and　driving　safety.　However,　it　is　urgent　to　investigate　intelligent　control　algorithms　to　improve　the　adaptability　of　CCC　in　complex　traffic　environment.　In　addition,　the　effect　of　communication　delays　attributed　to　shared　wireless　communications　on　the　performance　degradation　of　the　intelligent　CCC　design　cannot　be　ignored.　In　this　study,　the　design　of　deep　reinforcement　learning　(DRL)　controller　for　CCC　system　in　high-dynamic　traffic　scenarios　is　investigated,　which　considers　both　time-varying　leading　velocity　and　communication　delays.　To　be　more　specific,　an　intelligent　CCC　algorithm　based　on　deep　deterministic　policy　gradient　(DDPG)　is　developed.　According　to　the　training　samples　obtained　from　interacting　with　the　traffic　environment,　the　actor　network　and　the　critic　network　are　trained　to　maximize　the　quadratic　reward　function　determined　by　state　errors　and　control　inputs　for　generating　intelligent　control　strategies.　In　particular,　the　effect　of　previous　control　strategies　is　considered　in　vehicle　dynamics　analysis,　optimization　problem　formulation　and　Markov　decision　process　(MDP)　definition　to　compensate　the　performance　degradation　attributed　to　communication　delays.　Lastly,　the　effectiveness　and　convergence　of　the　proposed　DRL-based　CCC　controller　are　verified　through　numerical　simulations　with　various　conditions.　The　superior　performance　of　the　proposed　algorithm　is　shown　by　comparing　with　existing　traditional　algorithms　and　state-of-the-art　DRL　algorithms.