Nonlocal modified gravity without matter, where nonlocality is of the form $R^{-p}\cal{F}(\Box)R$ is considered from the cosmological point of view. Equations of motion are derived. Cosmological solutions of the form $a(t)=a_0|t-t_0|^\alpha,$ for the FLRW metric and curvature constant $k =0,\pm1$, are found.