The ignition delay time is an important factor to understand the combustion characteristics of internal combustion engine. In this study, ignition delay times of cool and thermal flame were observed separately in homogeneous charge compression ignition(HCCI) engine. This study presents numerical investigation of ignition delay time of n-heptane and alcohol(ethanol and n-butanol) binary fuel. The $O_2$ concentration in the mixture was set 9-10% to simulate high exhaust gas recirculation(EGR) rate condition. The numerical study on the ignition delay time was performed using CHEMKIN codes with various blending ratios and EGR rates. The results revealed that the ignition delay time increased with increasing the alcohol fraction in the mixture due to a decrease of oxidation of n-heptane at the low temperature. From the numerical analysis, ethanol needed more radical and higher temperature than n-butanol for oxidation. In addition, thermal ignition delay time is sharply increasing with decreasing $O_2$ fraction, but cool flame ignition delay time changes negligibly for both binary fuels. Also, in high temperature regime, the ignition delay time showed similar tendency with both blends regardless of blending ratio and EGR rate.