In　this　paper,　we　study　the　occurrence　mechanism　on　the　phenomenon　of　concentration　and　the　formation　of　delta-shock　wave　in　vanishing　adiabatic　exponent　limit　of　Riemann　solutions　to　the　Aw–Rascle　model　of　traffic　flow　with　a　relaxation　term.　At　first,　by　a　special　type　of　variable　substitution,　the　Riemann　problems　of　pressureless　gas　dynamics　and　Aw–Rascle　model　of　traffic　flow　with　a　relaxation　term　are　solved.　Unlike　the　homogeneous　case,　both　Riemann　solutions　are　no　longer　self-similar　due　to　the　relaxation　term.　Then,　we　rigorously　prove　that,　as　the　adiabatic　exponent　vanishes,　the　Riemann　solution　containing　a　shock　curve　and　a　contact　discontinuity　of　the　Aw–Rascle　model　with　a　relaxation　term　tends　to　a　special　delta-shock　wave,　which　is　different　from　the　delta-shock　wave　of　limiting　pressureless　gas　dynamics　model.　At　last,　some　numerical　simulations　are　presented　to　show　the　formation　process　of　delta-shock　waves　and　illustrate　the　above　analysis.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.