We study the $W^+W^-$ and $Z^0Z^0$ electroweak boson production in double parton scattering using QCD evolution equations for double parton distributions. In particular, we analyze the impact of splitting terms in the evolution equations on the double parton scattering cross sections. Unlike the standard terms, the splitting terms are not suppressed for large values of the relative momentum of two partons in the double parton scattering. Thus, they play an important role which we discuss in detail for the single splitting contribution to the cross sections under the study.