The behaviors of lattice distortions in the spin 1/2 antiferromagnetic XY model with Thue-Morse quasiperiodic modulation are investigated by the method of exact diagonalization. It is found that the lattice distortion at each site has the character intermediate between the periodic and random systems. For weaker or stronger quasiperiodic modulation, the lattice distortion may increase or decrease with strengthening of the modulation amplitude, respectively. The results also indicate that the energy gaps of ground states are strongly affected by the quasiperiodic modulation