Experimental determination of the effects of conjugated linoleic acid (CLA) and glycerol on the rate of enzymatic transesterification were studied to propose suitable mechanistic steps and generate a kinetic model. CLA was suggested due to its purported health benefits and application in preparation of functional foods. CLA, glycerol, and sunflower oil blends with varying concentrations were reacted using a 1, 3-specific immobilized lipase from Rhizomucor mehei. Scrutiny for mass transfer effects showed that esterification reaction was kinetically controlled. The reaction rate was determined, which showed that affinity of enzyme to CLA is lower than to glycerol. The transesterified lipids were analyzed by gas chromatography for composition of fatty acids and were evaluated for the free fatty acids (FFA). The esterification reaction kinetic follows the Ping Pong Bi Bi mechanism with competitive full (dead end) inhibition by acyl acceptors characterized by the V-max, K-mCOOH, K-mG, and K-IG values of 0.328 (mol/L/h), 0.342 (mol/L), 0.04526 (mol/L), and 0.329 (mol/L), respectively. Kinetic model study results indicated how FFAs (CLA and other FFAs) and triacylglycerols (sunflower molecules) can participate as the first substrate in the reaction to produce enriched triacylglycerols as the functional oil.