Gauge fluxes can be used to break the GUT gauge group in F-theory. We consider a non-abelian gauge flux associated to a poly-stable bundle with the structure SU(2)XU(1)XU(1), which is constructed by using a stable SU(2) bundle and two supersymmetric line bundles. Then we approach the Minimum Supersymmetric Standard Model (MSSM) from an E_6 GUT by using the spectral cover construction and this non-abelian gauge flux. Starting with an E_8 singularity, we obtain a rank 5 model with the gauge group SU(3) X SU(2) X U(1)2 by using an SU(3) spectral cover and the non-abelian flux.