In this paper, we have proposed $SU(2)$ non-Abelian electromagnetism gauge theory. In the theory, photon has self-interaction and interaction, which can explain photon entanglement phenomenon in quantum information. Otherwise, we find there are three kinds photons $γ^{+}$, $γ^{-}$ and $γ^{0}$, and they have electric charge $+e_γ$, $-e_γ$ and $0$, respectively, which are accordance with some experiment results.
