Abstract：In this work, we present the immersed finite element (IFE) method to solve time fractional diffusion equation with discontinuous coefficients, in which the Caputo fractional derivative is approximated by nonunform L1 scheme to deal with singularity of solution. For interface problems caused by discontinuous coefficients in space, we adopt the nonconforming immersed finite element method to discrete. Then the stabilities under 𝐿𝐿2(𝛺𝛺) norm and broken 𝐻𝐻1(𝛺𝛺) seminorm of fully discrete scheme are analyzed. Based on these results, the error estimates in 𝐿𝐿2(𝛺𝛺) norm and broken 𝐻𝐻1(𝛺𝛺) seminorm of fully immersed finite element scheme are obtain. Finally, several numerical examples are presented to illustrate the theoretical results.