Fractional　differential　equations　have　been　proved　to　be　powerful　tools　for　modelling　anomalous　diffusion　in　many　fields　of　science　and　engineering.　However,　when　comes　to　the　anomalous　diffusion　characterized　by　two　or　more　scaling　exponents　in　the　mean　squared　displacement　(MSD),　or　even　by　logarithmic　time　dependency　of　the　MSD,　distributed-order　diffusion　equations　are　shown　to　be　more　useful　than　the　general　single　or　multi-term　fractional　diffusion　equations.　In　this　paper,　we　construct　a　novel　finite　volume　method　for　solving　a　nonlinear　two-sided　space　distributed-order　diffusion　equation　with　variable　coefficients.　Firstly,　we　apply　the　modified　Gaussian　integral　formula　to　approximate　the　distributed-order　integral.　Secondly,　we　propose　the　finite　volume　method　based　on　a　piecewise-linear　polynomial　to　discretize　the　problem　and　establish　the　Crank–Nicolson　scheme.　Furthermore,　we　prove　that　the　proposed　method　is　stable　and　convergent　with　second　order　accuracy　in　both　space　and　time.　Finally,　some　numerical　examples　are　given　to　show　the　efficiency　of　the　proposed　method.　©　2020　Elsevier　B.V.