In　this　paper,　we　consider　the　time-space　fractional　diffusion　equation　on　a　bounded　interval　with　the　Caputo　time　fractional　derivative　and　the　two-sided　Riemann-Liouville　spatial　fractional　derivative.　|The　diffusion　coefficients　are　variable　with　respect　to　x　and　t.　The　temporal　non-uniform　L1-type　discretization　and　the　finite　volume　method　based　on　the　nodal　basis　functions　are　adopted　to　discrete　this　fractional　partial　derivative　equation.　We　strictly　prove　that　our　scheme　is　conditionally　stable　with　convergence　rate　O　(h2　+　N-min{2-alpha,r　alpha}),　where　h　is　the　spatial　step　and　N,　alpha,　r　are　the　temporal　nodal　numbers,　the　fractional　parameter　and　the　graded　parameter　respectively.　Finally,　some　numerical　results　are　presented　to　validate　the　theoretical　analysis.(c)　2023　Elsevier　B.V.　All　rights　reserved.