Near barrier fusion excitation function of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>6</mml:mn></mml:mmultiscripts><mml:mo>+</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>208</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>

The fusion cross sections of $^{6}\mathrm{Li}+^{208}\mathrm{Pb}$ system at energies near the barrier have been measured by means of the evaporation residue method and have been calculated in terms of the coupled-channels model, taking into account single and double phonon octupole excitations of $^{208}\mathrm{Pb}$ and the ${3}^{+}$ rotational state of $^{6}\mathrm{Li}$. By comparing the experimental results with the theoretical calculations and with the fusion cross section of $^{16}\mathrm{O}+^{208}\mathrm{Pb}$, in which no breakup happens, we conclude that the fusion cross sections of $^{6}\mathrm{Li}+^{208}\mathrm{Pb}$ are suppressed at above-barrier energies due to the effects of $^{6}\mathrm{Li}$ breakup, but below the barrier, the effects of breakup are not clear.