We investigate the phonon transmission and thermal conductance in a general Fibonacci quasicrystal by the model of lattice dynamics and the technique of transfer matrix.It is found that quasiperiodic distribution of masses may greatly destroy the phonon transport at both low and high frequencies and thus may affect the thermal conductance.The thermal conductance increases with temperature at low temperatures and displays saturation with further increase of the temperature.Such saturation behaviour is preserved even when the mass ratio of atoms in the Fibonacci chain is changed.