The load-displacement curves, elastic modulus, indent morphology, nanohardness and elastic recovery of high purity Molybdenum-Niobium single crystal were investigated by nanoindentation and scanning probe microscopy. The results show that Mo - Nb single crystal has a good plastic deformation ability. Mo-Nb crystal plane undergo elastic deformation and plastic deformation during the loading-unloading process, and the load-displacement curve do not show discontinuity, which demonstrates that cracks and brittle fracture are not formed in the indents. Moreover, the pile-up behavior around indents reveals that Mo-Nb single crystal has the low work hardening tend. The nanohardness and elastic modulus of Mo-Nb single crystal were measured by continuous stiffness measurement (CSM), and a size effect on the nanohardness and elastic modulus was observed, which decrease with the increase of indentation depth. The relationship the different nanohardness and elastic modulus is: (110) crystal plane > (112) crystal plane > (111) crystal plane. The Nix-Gao model was employed to analyze the nanoindentation mechanical characteristics of Mo-Nb single crystal, and the intrinsic hardness in the limit of infinite depth (H_0) are 3.96GPa, 2.61GPa and 3.47GPa, respectively; the size effect index(i) were calculated to be 0.18, 0.16 and 0.18, respectively. The characteristic length(h^*) of (110), (111), (112) crystal plane are 1196 nm, 2753nm and 1559 nm, respectively. Mo-Nb single crystal has a significant size effect when the indentation depth is below the characteristic length, and the size effect becomes more insignificant when indentation depth is deeper than the characteristic length. The nanoindentation size effect will disappear as the impression are deeper than 4106nm、5645nm和4693nm, respectively.