  We present the results of our QCD analysis for polarized quark distribution
and structure function $xg_1 (x,Q^2)$. We use very recently experimental data
to parameterize our model. New parameterizations are derived for the quark and
gluon distributions for the kinematic range $x \epsilon [10^{-8},1]$, $Q^2
\epsilon [1,10^6]$ GeV^2. The analysis is based on the Jacobi polynomials
expansion of the polarized structure functions. Our calculations for polarized
parton distribution functions based on the Jacobi polynomials method are in
good agreement with the other theoretical models. The values of $\Lambda_{QCD}$
and $\alpha_s(M_z)$ are determined.
