  Presented here is a calculation of inelastic $J/\psi$ production in polarized
photon-hadron collisions under the framework of NRQCD factorization formalism.
We consider the photoproduction of $\jpsi$ in the energy range relevant to
HERA. The Weizs\"acker-Williams approximation is adopted in the evaluation of
the cross sections for $ep$ collisions. We found that this process can give
another independent test for the color-octet mechanism, and the different
features for the two color-octet processes may provide further informations on
the mechanism for inelastic $\jpsi$ photoproduction. And the discrepancy on the
production asymmetry $A$ between various sets of polarized gluon distribution
functions is also found to be distinctive.
