We demonstrate a new method of extracting parton distributions 
from lattice calculations, based on concepts of pseudo-PDFs and 
Ioffe-time distributions (ITD).  Our lattice calculation  shows  
a linear component in the  exponential  z_3-dependence 
in the rest-frame ITD   expected from  the Z(z_3) factor 
generated by the gauge link. We also observe that this   
factor disappears in the ratio of ITDs  taken at different Ioffe times \nu=Pz_3. 
When plotted as a function of the Ioffe time  and z_3, the data  
are very close   to z_3-independent functions which allows us to 
extract PDFs.  Our curve for u_v(x)-d_v(x) is  rather close
to  experimental global fits. For small z_3,  we observe  perturbative 
DGLAP evolution of pseudo-PDFs,  with  \alpha_s/\pi =0.1.