  In order to get information about the polarized gluon distribution in a
proton, we studied the electroproduction of \psi' in polarized electron and
polarized proton collisions in the framework of the NRQCD factorization
approach. The value of the cross section d\Delta\sigma / dp_T^2 for color-octet
mechanism is about 5 times larger than that for color-singlet one, and it might
be another test of the color-octet model if the polarized gluon distribution
\Delta g(x) is well known. Furthermore, we found that this reaction is quite
effective for testing the model of gluon polarization by measuring the double
spin asymmetry A_{LL} for the initial electron and proton. Though the shape of
p_T^2 distribution of A_{LL} is quite similar for the production mechanism with
color-octet and color-singlet, we can see a big difference in A_{LL} among
various models of the polarized gluon distribution function \Delta g(x).
