We use ab initio calculations to analyze the influence of 4d and 5d transition metal alloying elements on cohesive properties of the bulk and a representative grain boundary in Cr within the framework of the Rice–Thomson–Wang approach. The results obtained for Cr are combined with the analogous results for Ni to select Ta and Nb as promising alloying additions to dual-phase (α/γ) Cr-Ni-base high-temperature alloys. Ta and Nb are added to the alloying system of an existing alloy I (Cr-Ni-W-V-Ti) in an attempt to design a chemical composition of a new alloy II (Cr-Ni-W-V-Ti) + (Ta-Nb). Investigation of the microstructure of the Ta-bearing Cr-Ni-alloy reveals a Ta enrichment of large γ-areas near GBs in α-matrix that we consider as potency to increase the cohesive strength of GBs and the cohesive energy of the bulk in γ-phase. Mechanical testing of alloys I and II demonstrates that the alloy II has improved tensile strength and creep resistance at high temperatures.