The　pullback　attractors　for　the　2D　nonautonomous　g-Navier-Stokes　equations　with　linear　dampness　are　investigated　on　some　unbounded　domains.　The　existence　of　the　pullback　attractors　is　proved　by　verifying　the　existence　of　pullback　D-absorbing　sets　with　cocycle　and　obtaining　the　pullback　D-asymptotic　compactness.　Furthermore,　the　estimation　of　the　fractal　dimensions　for　the　2D　g-Navier-Stokes　equations　is　given.