The phase behavior of asymmetrically interacting ABC star triblock copolymer melts is investigated by the self-consistent field theory (SCFT). Motivated by the experimental systems, in this study, we focus on the systems in which the Flory-Huggins interaction parameters satisfy chi(AC) > chi(BC) approximate to chi(AB). Using various initialization strategies, a large number of periodic structures have been obtained in our calculations. A fourth-order pseudospectral algorithm combined with Anderson mixing method is used to compute the free energy of candidate structures carefully. The stability has been analyzed in detail by splitting the free energy into internal and entropic parts. A complete and complex triangular phase diagram is presented for a model with chi(AC) > chi(BC) = chi(AB) in which 15 ordered phases, including two- and three-dimensional structures, have been predicted to be stable from the SCFT calculations. Generally speaking, with the asymmetrical interactions, the hierarchical structures tend to be formed near the B-rich corner of the triangular phase diagram. This work broadens the previous theoretical results from equal interaction systems to unequal interaction systems. The predicted phase behavior is in good agreement with experimental observations and previous theoretical results.