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In this article, a Galerkin finite element method combined with second-order time discrete scheme for finding the numerical solution of nonlinear time fractional Cable equation is studied and discussed. At time , a second-order two step scheme with -parameter is proposed to approximate the first-order derivative, and a weighted discrete scheme covering second-order approximation is used to approximate the Riemann-Liouville fractional derivative, where the approximate order is higher than the obtained results by the L1-approximation with order ( in the existing references. For the spatial direction, Galerkin finite element approximation is presented. The stability of scheme and the rate of convergence in -norm with $ O(\Delta t^2+(1+\Delta t^{-\alpha})h^{m+1})$ are derived in detail. Moreover, some numerical tests are shown to support our theoretical results.