A computational analysis has been made on fluid flow in a regenerative cooling Passage for a reduced size liquid rocket engine to predict pressure drop and heat transfer rate in it. The contraction/expansion of the cross sectional area of the passage turn out to increases both the pressure loss and the heat transfer rate of the duct. The changes of the cross sectional area near the nozzle throat are effective to protect the throat which suffers from severe thermal load. Also given is the qualitative characteristics of the performance of the regenerative cooling system due to the variation of coolant flow rate.