In　this　paper,　the　well-posedness　for　the　non-autonomous　reaction-diffusion　equation　with　infinite　delays　on　a　bounded　domain　is　established.　The　existence　of　pullback　attractors　for　the　process　in　C-gamma,　L-r(Omega)　or　C-gamma,　W-1,W-　r(Omega)　is　proved,　respectively.　The　noncompact　Kuratowski　measure　is　applied　to　check　the　asymptotic　compactness.