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We investigate the renormalization group of the generalized Fibonacci lattices associated with the aperiodic sequences as constructed by the inflation rule: {A,B} --> {A(n)B(m),A}, in which m and n are positive integers. The derived renormalization group consists of 2n(n+m-1)+1 basic renormalization-group transformations. By suitable combinations of these basic transformations, local Green's function and local density of states at any sites can be calculated for electrons on the generalized Fibonacci lattices. The off-diagonal model is employed, and the local electronic densities of states at several sites are numerically calculated for some generalized Fibonacci lattices.