With the aim of the efficient use of plant oils as alternative fuels, the deoxygenation of saturated and unsaturated triglycerides in a catalytic cracking process was investigated using a fluid catalytic cracking catalyst with enhanced hydrogen-transfer activity. The decomposition and deoxygenation of sun flower oil (unsaturated triglycerides) proceeded rapidly and produced a large amount of aromatic hydrocarbons, which are unsuitable for fuel applications. In contrast, the rate of deoxygenation of coconut oil (saturated triglycerides) was slow and some oxygen-containing species were observed as products. During the co-processing of saturated and unsaturated triglycerides, the deoxygenation of saturated triglycerides was accelerated and complete deoxygenation was achieved. The acceleration of the deoxygenation reaction was attributed to the rapid formation of hydrogen donors, such as olefins and naphthenes, from the decomposition of unsaturated triglycerides. The olefins and naphthenes released hydrogen species by cyclization and aromatization reactions. These hydrogen species then reacted with saturated triglycerides and their derivatives (fatty acids and aldehydes) in hydrogen-transfer reactions, accelerating the hydrodeoxygenation of saturated triglycerides. The hydrodeoxygenation of saturated triglycerides produced paraffins and olefins rather than aromatics. The increase in the amount of paraffins and olefins produced by the accelerated deoxygenation of saturated triglycerides was larger than the amount of aromatic hydrocarbons derived from unsaturated triglycerides. Thus, co-processing of saturated and unsaturated triglycerides was confirmed to be effective for simultaneously achieving both the acceleration of saturated triglyceride deoxygenation and the suppression of aromatic hydrocarbon formation.