The invention is directed to CLA-rich vegetable oil production from linoleic rich oils by heterogeneous catalysis. The process produces conjugated PUFA in triglyceride form, preferably at least 20% CLA-rich, by isomerization of a non-conjugated PUFA in vegetable oils using a heterogeneous transition metal catalyst promoted by an organic acid and/or thiol-containing compound. The heterogeneous catalysis isomerization process can use steam/vacuum distillation, hydrogenation unit and/or deodorization to produce CLA-rich soy oil. After processing, any catalyst residue may be removed by filtration, beaching, deodorizing, adsorbents or centrifugation to obtain high quality, CLA-rich oils
