In　this　article,　a　generalized　log　orthogonal　functions　(GLOFs)-spectral　collocation　method　to　two　dimensional　weakly　singular　Volterra　integral　equations　of　the　second　kind　is　proposed.　The　mild　singularities　of　the　solution　at　the　interval　endpoint　can　be　captured　by　Gauss-GLOFs　quadrature　and　the　shortcoming　of　the　traditional　spectral　method　which　cannot　well　deal　with　weakly　singular　Volterra　integral　equations　with　limited　regular　solutions　is　avoided.　A　detailed　L　infinity$$　{L}＜^＞{\infty　}　$$　convergence　analysis　of　the　numerical　solution　is　carried　out.　The　efficiency　of　the　proposed　method　is　demonstrated　by　numerical　examples.