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This paper presents the design optimization of a heat exchanger for a free-piston Stirling engine (FPSE) through an improved quasi-steady flow (iQSF) model and a central composite design. To optimize the tubular hot heat exchanger (HHX) design, a design set of central composite designs for the design factors of the HHX was constructed and the brake power and efficiency were predicted through the iQSF model. The iQSF model is improved because it adds various heat and power losses based on the QSF model and applies a heat transfer model that simulates the oscillating flow condition of an actual Stirling engine. Based on experimental results from the RE-1000, an FPSE developed by Sunpower, the iQSF model significantly improves the prediction error of the indicated power from 66.9 to 24.9% compared to the existing QSF model. For design optimization of the HHX, the inner diameter and the number of tubes with the highest brake power and efficiency were determined using a regression model, and the tube length was determined using the iQSF model. Finally, the brake output and efficiency of FPSE with the optimized HHX were predicted to be 7.4 kW and 36.4%, respectively, through the iQSF analysis results.