We　study　the　traffic-driven　epidemic　spreading　on　scale-free　networks　with　tunable　degree　distribution.　The　heterogeneity　of　networks　is　controlled　by　the　exponent　γ　of　power-law　degree　distribution.　It　is　found　that　the　epidemic　threshold　is　minimized　at　about　γ=2.2.　Moreover,　we　find　that　nodes　with　larger　algorithmic　betweenness　are　more　likely　to　be　infected.　We　expect　our　work　to　provide　new　insights　in　to　the　effect　of　network　structures　on　traffic-driven　epidemic　spreading.　©　2016　World　Scientific　Publishing　Company.