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Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in \(L^{1}(H^{1})\)-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order \(\mathcal{O}(\tau ^{2}+h^{m+1})\) is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.

Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation