The effect of quasiperiodic interaction on lattice distortion and energy gap in spin-Peierls model is studied by exact diagonalization and self-consistent methods. It is shown that quasiperiodic interaction can result in self-similar characteristics for lattice distortion and energy spectra of spin-Peierls model. Moreover, we find that the average value of lattice distortion will be increased, decreased or increased firstly then decreased as quasiperiodic interaction strength is enhanced. Such kind of behavior strongly depends on the lattice spring constant K. The energy gap also displays similar behavior.