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• The multiple heterostructure is realized in TiZrNbTa refractory high-entropy alloy via composition and annealing design. • The strength-ductility trade-off over a wide strain rate range of TiZrNbTa refractory high-entropy alloy is overcome by the multiple heterostructures. • The quasi-static tensile yield strength, ultimate tensile strength and elongation are 18 %, 20 % and 50 % higher than those of the base alloy. • A combination of high yield strength (∼1450 MPa) and large ultimate strain (∼25 %) is achieved at high strain rate (103 s−1). To improve the mechanical properties of refractory high-entropy alloy (RHEA), whose strain hardening capacity is relatively weak, over a wide strain rate range, the multi-heterostructure strategy is investigated in this work. Based on the composition and annealing design, the multi-heterostructure consisting of two mutually coherent body-centred cubic solid solution matrices and penetrating complex phases is achieved in TiZrNbTaNi 0.05 RHEA (MH-RHEA). Under quasi-static loading, this multi-heterostructure takes both good precipitation strengthening and hetero-deformation-induced hardening effects, diversifies the deformation modes, finally promotes the strain hardening capacity and deformation homogeneity. The tensile yield strength, ultimate tensile strength and elongation of MH-RHEA are 1195 ± 12 MPa, 1235 ± 9 MPa and 22.4 ± 1.0 %, respectively, which are 18 %, 20 % and 50 % higher than those of the base alloy. Under dynamic loading (∼103 s−1), the thermal effect can be neutralized and the deformation localization is avoided. Consequently, a high yield strength of ∼1450 MPa and a large ultimate strain of ∼25 % without fracture at a high strain rate of 2390 s−1 are realized in MH-RHEA. This heterostructure strategy offers a new paradigm to enhance the strength and ductility simultaneously of RHEAs over a wide strain rate range. [Display omitted] [ABSTRACT FROM AUTHOR]