Let G be a simple undirected graph, and Gϕ be a mixed graph of G with the generalized orientation ϕ and Hermitian-adjacency matrix H(Gϕ). Then G is called the underlying graph of Gϕ. The Hermitian energy of the mixed graph Gϕ, denoted by EH(Gϕ), is defined as the sum of all the singular values of H(Gϕ). A k-regular mixed graph on n vertices having Hermitian energy is called a k-regular optimum Hermitian energy mixed graph. Liu and Li (2015) [11] proposed the problem of determining all the k -regular connected optimum Hermitian energy mixed graphs. This paper is to give a solution to the problem for the case k=3.