We study the superfluid behavior of a population imbalanced ultracold atomic Fermi gases with a short range attractive interaction in a one-dimensional (1D) optical lattice,using a pairing fluctuation theory.We show that,besides widespread pseudogap phenomena and intermediate temperature superfluidity,the superfluid phase is readily destroyed except in a limited region of the parameter space.We find a new mechanism for pair hopping,assisted by the excessive majority fermions,in the presence of continuum-lattice mixing,which leads to an unusual constant Bose-Einstein condensate (BEC) asymptote for Tc that is independent of pairing strength.In result,on the BEC side of unitarity,superfluidity,when it exists,may be strongly enhanced by population imbalance.