In this letter, we report the results for the isovector polarized quark quasi-distribution functions Δu(x,v)−Δd(x,v) in the large-Nc limit, 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 PN→∞ (or the velocity v→1), compared to the case of the unpolarized isosinglet distributions.