The experimental realization of the effective spin-orbit (SO) coupling in quantum gases of untracold atoms has generate great interests in studying the many-body physics of this system. For a Rashba-type spin-orbit coupling, there is still a BEC-BCS crossover for the superfluid ground state though both singlet and triplet components appear in the pairing wave-function. Due to enhancement of the density state (DOS) at Fermi surface, the pairing gap is greatly increased for large SO coupling on the BCS side, while the increasing is less significant on the BEC side. The superfluid transition temperature is also greatly increased when SO coupling strength is large, and it can be enhanced to a sizable fraction of Fermi temperature even for a weak attractive interaction.