Multi-agent　deep　reinforcement　learning　(MADRL)　is　a　promising　learning-based　data-driven　approach,　particularly　when　it　is　applied　to　traffic　signal　control　(TSC)　in　a　large-scale　urban　road　network.　However,　the　present　MADRL-based　TSC　methods　still　deserve　further　studies　at　the　aspects　of　mutual　coordination　among　multiple　agents　and　computing　efficiency　of　training　algorithms.　In　this　study,　we　propose　an　adaptive　value　decomposition-based　multi-agent　actor-critic　(AVDMAC)　approach　using　a　parallel　training　algorithm　for　cooperative　traffic　network　flow　control.　Firstly,　the　original　centralized　actor-critic　reinforcement　learning　tasks　are　decomposed　into　several　local　learning　tasks,　where　each　actor-critic　agent　optimizes　its　control　decisions　in　response　to　local　environment　feedback.　Additionally,　multiple　agents　striving　towards　a　common　objective　are　coordinated　through　an　adaptive　factorization　model.　In　this　model,　weight　coefficients　are　adaptively　assigned　to　the　action-value　function　of　distributed　agents　by　aggregating　local　rewards,　so　as　to　form　a　global　joint　actionvalue　function　that　considers　the　individual　contribution　differences　among　local　decisions.　Further,　we　develop　the　parallel　training　formulations　and　implementation　algorithm　for　AVDMAC　approach　based　on　Spark　cloud　in　order　to　relieve　of　the　time　consumption　load　during　MADRL　training.　Numerical　experiments　demonstrate　the　advantages　at　convergence,　computational　efficiency,　and　control　performance　of　the　AVDMAC　approach.