The semiclassical closed-orbit theory begins to fail when the returning wave bec omes infinite near the core, and this is the typical situation when bifurcations of closed-orbits occur- We describe the phenomena of bifurcations and calculate the recurrence spectra of Li Rydberg atoms in the vicinity of the bifurcation e nergy using the uniform approximation method- The spectra with a constant energy ε=-2-94, and a constant scaled electric field 135-86-1/4<160 -11 are recorded and the effect of the core-scattering is taken into account- T he recurrence spectra are compared with those obtained by the primary extended c losed-orbit theory and those of hydrogen atoms- The results display the importan t contributions of bifurcations and core-scattering to the recurrence spectra of Li Rydberg atoms-