Copper-containing low-alloy steel based on the ASTM A707 5L grade is widely used for structural parts of offshore wells. However, it is difficult to stably obtain good weld joint toughness. With this background, this paper focuses on the metallurgical factors controlling the heat-affected zone (HAZ) toughness of A707 modified steel. Potential factors considered are the grain size, the martensite–austenite constituent (M-A), and precipitates. Thus, the purpose was to clarify the effect of M-A and precipitates on HAZ toughness. Furthermore, Cu, Si, and Mn contents, which affect M-A and precipitates generations, were focused on and tried to improve HAZ toughness by optimizing their contents in ASTM A707 steel. The weld test results showed that the toughness of an intercritically coarsened grain HAZ (ICRCGHAZ) was remarkably lower than that of the other heat cycle pattern due to the formation of M-A. It is, therefore, essentially important to suppress the formation of M-A in order to improve toughness in the HAZ of the steel. Therefore, the chemical composition was optimized in an effort to improve HAZ toughness. Copper had no negative influence on the HAZ toughness. It was found that when the Mn and Si contents of the steel decreased, the area fraction of M-A decreased. Consequently, the ICRCG HAZ toughness is improved because the toughness increases with the decrease in the area fraction of M-A. The recommended amounts of Cu, Mn, and Si to ensure HAZ toughness are more than 1.0 wt%, less than 0.6 wt%, and less than 0.1 wt%, respectively.