β-type Ti-29Nb-13Ta-4.6Zr alloy is a promising novel material for biomedical applications. We have proposed a 'single crystalline β-Ti implant' as new hard tissue replacements for suppressing the stress shielding by achieving a drastic reduction in the Young's modulus. To develop this, the orientation dependence of the plastic deformation behavior of the Ti-29Nb-13Ta-4.6Zr single crystal was first clarified. Dislocation slip with a Burgers vector parallel to <111> was the predominant deformation mode in the wide loading orientation. The orientation dependence of the yield stress due to <111> dislocations was small, in contrast to other β-Ti alloys. In addition, {332} twin was found to be operative at the loading orientation around [001]. The asymmetric features of the {332} twin formation depending on the loading orientation could be roughly anticipated by their Schmid factors. However, the critical resolved shear stress for the {332} twins appeared to show orientation dependence. The simultaneous operation of <111> slip and {332} twin were found to be the origin of the good mechanical properties with excellent strength and ductility. It was clarified that the Ti-29Nb-13Ta-4.6Zr alloy single crystal shows the "plastically almost-isotropic and elastically highly-anisotropic" nature, that is desirable for the development of 'single crystalline β-Ti implant'.