Achieving both low Young's modulus and high strength, which are essentially in a trade‐off relationship, is an important challenge in the field of biomaterials. Herein, the effects of oxygen and nitrogen addition on mechanical properties and recrystallization texture of a metastable Ti–18Zr–3Nb–3Sn–2Mo alloy are investigated. Both oxygen and nitrogen additions increase the apparent yield stress and tensile strength. The N‐added alloy exhibits an exceptionally strong {110}<001> texture, commonly referred to as Goss texture, leading to a lower Young's modulus when compared with the O‐added alloy. It is found that the formation and subsequent dissolution of the α‐phase plays an important role in the development of recrystallization texture. The {110}<001> texture can be enhanced in the O‐added alloy by a two‐step heat treatment, the first step to form the α‐phase and the second step to dissolve the α‐phase during recrystallization. An excellent combination of a low Young's modulus and a high yield stress is achieved in the O‐added alloy subjected to the two‐step heat treatment.