  A new model of QCD parton shower is proposed which is dedicated to two-photon
process in $e^+ e^-$ scattering. When hadron jets are produced, the photon may
resolve into quark-antiquark pairs so that the structure functions of the
photon should be introduced. Based on the Altarelli-Parisi equation for these
functions, an algorithm is formulated that allows us to construct a model for
parton showers for the photon. Our model consists of two parts, one of which
describes the deep inelastic scattering of the photon and the other one the
scattering of two quasi-real photons. Using the model some results are
presented on parton distributions and jet production.
