By means of the decomposition-decimation method based on the renormalization-group technique, we have studied the properties of electronic energy spectrum for the two-dimensional Fibonacci quasicrystals. It is found that the spectrum has a multifurcating structure which is very different from the monofurcating structure of one-dimensional Fibonacci quasicrystals. By using the four-fold symmetry of the Fibonacci quasilattice under study, we have reduced the Hamiltonian and then performed a numerical simulation, the results of which are consistent with the analytical ones.