Recently, the problem of the spontaneous breaking of both global and local symmetries of PT-symmetric Abelian gauge theories was considered. In this paper, we study problem of the spontaneous breaking of a PT symmetric non-Abelian SU(2) gauge theory. The non-Abelian PT symmetric theory includes two complex doublets and ? with interaction term. Because of the existence of the interaction term, this Lagrangian is non-Hermitian. In this theory at least two massless complex doublet fields and two massive complex doublet fields are needed. The Lagrangian of theory is invariant under SU(2) transformations. we show that in non-Hermitian theories described by the PT-symmetric Lagrangian after broking SU(2) continuous global symmetry spontaneously, three massless Goldeston bosons appear. Finally, we investigate the Higgs mechanism in this theory and obtain massive gauge fields.