  In this letter, we report the results for the isovector polarized quark
quasi-distribution functions $\Delta u(x,v) - \Delta d(x,v)$ in the large
$N_c$, calculated within the chiral quark-soliton model. It is shown that the
polarized quark quasi-distributions present good convergence to the light-cone
PDFs in the limit of the nucleon boost momentum $P_N \to \infty$ (or the
velocity $v \to 1$), compared to the case of the unpolarized isosinglet
distributions.
