I will review our research on quantum phase transition of spin-orbit coupling repulsive Fermi gas.We find that a strong spin-orbit coupling can considerably reduce the critical interaction strength for itinerant ferromagnetism transition,which provides a new and efficient mechanism to realize this long sought state.These novel phenomena could be detected by current experimental techniques such as speckle imaging [1].We investigate the fidelity susceptibility of a two-dimensional spin-orbit-coupled Fermi superfluid and the topological phase transition driven by a Zeeman field in the perspective of its ground state wave function.The topological phase transition can be detected by measuring the momentum distribution in cold atom experiments [2].We obtain the collective modes in the spin-orbit-coupled Fermi gas with repulsive s-wave interaction.We also propose an experimental protocol for detecting these collective modes and discuss corresponding experimental signatures in the ultra-cold Fermi gases experiment [3].We get the normal-state properties of spin-orbit-coupled Fermi gases with repulsive s-wave interaction,in the absence of molecule formation,i.e.,in the so-called “upper branch” [4].We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling.As a competition between spin-orbit coupling and population imbalance,the finite-temperature phase diagram reveals a large variety of new features,including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes [5].