This study was carried out to optimize premixed burner and heat exchanger of the condensing gas boiler which can save energy by utilizing latent heat of combustion gas and reduce pollutant in exhaust gas. The heat exchanger of the gas boiler was composed of three parts, which were an upper, lower, and coil heat exchanger. The upper heat exchanger was placed outside of the premixed burner and a lower heat exchanger was located under the upper heat exchanger. And, coil heat exchanger rounded the outer surface of an upper and lower heat exchanger. The boiler designed by this research reaches turn-down ratio 4:1 in the domain of equivalence ratio 0.75${~}$0.8 and thermal efficiency of $97\%$. Emission of NOx and CO concentration was under 20ppm and 140ppm at equivalence ratio 0.8. When diameter of the burner is replaced from 60mm to 50mm, emission of CO was reduced about 50ppm remarkably.