The incipient plasticity and creep behavior of body-centered cubic (BCC) Ti65(AlCrNb)35 medium entropy alloy (MEA) were investigated via nanoindentation. The elastic modulus and hardness obtained from different methods were compared. The activation volume for plastic deformation was calculated to be 11 b3, indicating a larger-scaled Peierls deformation mechanism typical for BCC metals. The orientation effect on incipient plasticity was studied on (100), (110) and (111) orientations at room temperature. The orientation difference is attributed to the different Schmid factors for different planes. The activation volume and activation energy of dislocation nucleation on Ti65(AlCrNb)35 was estimated as 0.8–0.9 b3 and 0.43 eV, which suggests that the mechanism of incipient plasticity is heterogeneous dislocation nucleation assisted by pre-exist defects, with a very localized activated volume. Also, the activation volume and energy of Ti65(AlCrNb)35 are higher than those of conventional metals (Ni, Pt, Cr and Mg) and lower than those of high entropy alloys (HEAs), which suggests that the dislocation nucleation in Ti65(AlCrNb)35 is more difficult than that in metals but easier than that in HEAs. Creep responses of the (100), (110) and (111) grains at 500–600 °C were found to be all dominated by the power-law dislocation creep mechanism (stress exponent n ~ 5) with the activation energy ~130 kJ/mol. The high stress applied by the indenter tip led to the stress-induced pipe diffusion, assisting the dislocation climb and lowering the activation energy. The activation volume was measured as 3–6 b3, related to dislocation climb and atom diffusion at elevated temperatures. The creep displacements and creep rates for the (100), (110) and (111) planes are quite similar, probably resulting from (i) complex slip systems in BCC structure underneath the indenter tip, (ii) a complex strain field produced by concentrated solute atoms, and (iii) the stress-induced pipe diffusion.