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Mo-based single crystal is a key material for nuclear power generation components in deep space exploration ships. Optimizing alloy composition is an important way to the applied property improvement of single crystal materials, and also can improve the power generation efficiency and service life of nuclear power sources. In this paper, a novel Mo-Nb-W single crystal was prepared by electron beam suspension zone melting method, and the hardness (H), contact stiffness (S) and elastic modulus (E) in the (110), (111) and (112) orientation crystal planes were investigated by nanoindentation technology. The results showed that there was no pop-in phenomenon in the load-displacement (P-h) curves of the (111) crystal plane, while the pop-in step appeared in the P-h curves of both (110) and (112) crystal plane during nanoindentation. The hardness in the measured oriented crystal planes gradually gone up with the increase of strain rate due to the shortened relaxation time, while the contact stiffness and elastic modulus slowly decreased as strain rate increased. There was significant anisotropy in the mechanical properties of Mo-Nb-W single crystal, and the hardness ranked: H(111)>H(110)>H(112), while the order of contact stiffness and elastic modulus were as follow: S(111)>S(112)>S(110) and E(111)>E(112)>E(110). The hardness in these mentioned orientation crystal planes gradually decreased with the rising of indentation depth, and the (111) oriented crystal plane had the most obvious indentation size effect.