The Generalized Empirical Interpolation Method (GEIM, [12]) is an extension first presented in [12] of the classical Empirical Interpolation Method (see [1], [8], [15]). It replaces values at interpolation points by evaluations from continuous linear forms, which allows, in particular, to relax the classical continuity constraint in the functions to interpolate. These functions are members of a compact subset F of a Banach or Hilbert space with a small Kolmogorov n-width and the quality of the approximation strongly depends on the choice of the interpolating functions and linear forms. For this reason, the purpose of this work is to provide a priori convergence rates for the GEIM that proposes a greedy algorithm to choose these interpolation couples. We show that, when the Kolmogorov n-width of F decays polynomially or exponentially, the interpolation error has the same behavior modulo the norm of the interpolation operator of GEIM. Sharper results will also be obtained in the situation when the ambient space is a Hilbert.