Many temperature-related problems are created in asphalt pavement due to the low temperature. In particular, loss of tensile strength due to low temperature is known to be responsible for thermal failure of pavements in cold regions under $-20^{circ}C$. The objective of this study is to evaluate characteristics of resistance against low-temperature cracking of polymer asphalt concrete mixtures modified with LDPE and SBS. The test results showed that the mixtures had the maximum indirect tensile strength(ITS) at low temperature ranging from $-10^{circ}C. It was proved through ITS test that the stress due to differential thermal contraction over the tensile strength did generate internal damage at the temperature below $-20^{circ}C$. It was shown that the asphalt mixtures modified with polymer had better ITS than the normal asphalt mixture at the temperature below $-20^{circ}C$. Thus the effect of modification was revealed as tensile strength improvement. From the results of this study, it was recommended that polymer-modified asphalt should be used in order to prevent low-temperature cracking in cold region.