Abstract: Using the general theory of constructing shifted derived Poisson algebra from a Lie algebra pair, the \left( + 1\right) -shifted derived Poisson algebras arising from a special class of Lie algebra pairs (\mathfrakg,\mathfrakh) are given explicitly. Here \mathfrakg is a complex semi-simple Lie algebra, and the Lie subalgebra \mathfrakh of \mathfrakg is the direct sum of a Cartan subalgebra and a positive root space.