An　efficient　method　is　examined　for　the　Oldroyd　fluid　which　belongs　to　nonlinear　integro-differential　equations.　This　approach　is　approximately　discretized　by　the　FEM　(i.e.　finite　element　method)　in　space　level,　and　a　second-order　Crank–Nicolson　extrapolation　in　time.　It　reduces　nonlinear　equations　to　linear　equations.　Thus　can　greatly　increase　the　computational　efficiency.　In　order　to　approximate　the　integral　term,　we　apply　the　＇midpoint　rule＇　approach.　The　error　of　the　integral　term　to　the　midpoint　rule　is　determined.　We　establish　that　the　method　is　unconditionally　stable　and　convergent.　The　L2-optimal　error　estimate　with　second　order　accuracy　in　time　and　space　level　is　obtained　without　imposing　any　restriction　on　time-step　size,　while　all　previous　works　of　higher-order　scheme　require　certain　time-step　conditions.　Moreover,　corresponding　numerical　experiments　are　shown　to　demonstrate　the　accuracy,　the　unconditional　stability　and　convergence　of　this　method　for　the　Oldroyd　fluid.　The　structure　is　also　suitable　for　the　Navier–Stokes　equations　(i.e.　ρ=0　in　the　Oldroyd　fluid).　©　2022　Elsevier　B.V.