A newly revised inverse scattering transform(IST) for the derivative nonlinear Schrdinger(DNLS+) equation with non-vanishing boundary condition(NVBC) and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST. A newly revised inverse scattering transform (IST) for the derivative nonlinear Schrödinger (DNLS +) equation with non-vanishing boundary condition (NVBC) and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern. explicit breather-type one-soliton solution, which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary, has been derived to verify the validity of the revised IST.