The invention provides a bio-Co-Cr-Mo alloy with ion elution suppressed by regulation of texture, and process for producing the same. This invention provides a technique for rendering bio-toxicity such as allergy toxicity derived from Ni trace impurity, i.e., nickel toxicity, which is unavoidably present in a bio-Co-Cr-Mo alloy or an Ni-free stainless steel alloy unharmful, characterized in that an element selected from the group consisting of the group IVA, VA and IIIB elements of the periodic table, particularly an element selected from the group consisting of the group IVA elements of the periodic table, is added to the alloy composition. The additive element is preferably an element selected from the group consisting of zirconium and titanium, more preferably zirconium.