Diffuse　optical　tomography　(DOT)　is　a　promising　non-invasive　optical　imaging　technology　that　can　provide　functional　information　of　biological　tissues.　Since　the　diffused　light　undergoes　multiple　scattering　in　biological　tissues,　and　the　boundary　measurements　are　limited,　the　inverse　problem　of　DOT　is　ill-posed　and　ill-conditioned.　To　overcome　these　limitations,　inverse　problems　in　DOT　are　often　mitigated　using　regularization　techniques,　which　use　data　fitting　and　regularization　terms　to　suppress　the　effects　of　measurement　noise　and　modeling　errors.　Tikhonov　regularization,　utilizing　the　L2　norm　as　its　regularization　term,　often　leads　to　images　that　are　excessively　smooth.　In　recent　years,　with　the　continuous　development　of　deep　learning　algorithms,　many　researchers　have　used　Model-based　deep　learning　methods　for　reconstruction.　However,　the　reconstruction　of　DOT　is　solved　on　mesh,　arising　from　a　finite　element　method　for　inverse　problems,　it　is　difficult　to　use　it　directly　for　convolutional　network.　Therefore,　we　propose　a　model-based　graph　convolutional　network　(Model-GCN).　Overall,　Model-GCN　achieves　better　image　reconstruction　results　compared　to　Tikhonov,　with　lower　absolute　bias　error　(ABE).　Specifically,　for　total　hemoglobin　(HbT)　and　water,　the　average　reduction　in　ABE　is　68.3%　and　77.3%,　respectively.　Additionally,　the　peak　signal-to-noise　(PSNR)　values　are　on　average　increased　by　6.4dB　and　7.0dB.