We investigate the itinerant ferromagnetism of repulsively interacting Fermi gases with spin-orbit coupling (SOC). We find that the spin-orbit coupling provides a new and efficient mechanism to realize the itinerant ferromagnetism (FM) which is a long sought state in material science at much weaker repulsive interactions. We classify the symmetries and symmetry breaking of the SOC Hamiltoniian and find their exact constraints on the density-spin response functions. In the para-magnet side, the SOC leads to the splitting of two transverse modes. In the FM side, the Fermi surfaces acquire a finite momentum and also experience a topological Lifshitz transition, the symmetry breaking leads to one gapped transverse pseudo-Goldstone mode instead of one gapless Goldstone mode. Various experimental probes are discussed.