Offshore structures are exposed to severe operating conditions because energy resource development has recently extended toward deeper seabed and lower temperature regions. Hence, fracture toughness evaluation for very thick and high strength steels is one of the most important parameters required for the structural integrity assessment of offshore structures. Fracture toughness is known as a property which describes the ability of a material containing a crack to resist unstable brittle fracture. Crack tip opening displacement (CTOD) and J integral are the most commonly employed parameters as fracture criteria in elastic plastic fracture mechanics (EPFM). There have been extensive research efforts to clarify the relationship between CTOD and J integral in elastic plastic regime. Plastic constraint factor (PCF) in the relationship between CTOD and J integral can serve as a parameter to characterize constraint effects in fracture involving plastic deformation. In this regard, the characteristics of the PCF are of significant importance in EPFM analysis. In this study, we evaluated fracture toughness of American Petroleum Institute (API) 2 W Gr. 50 steel in terms of CTOD in various temperatures using single edge notched bend (SENB) specimens. Test specimens are fabricated by submerged arc welding (SAW) and flux cored arc welding (FCAW). In addition, CTOD values are compared to absorbed impact energy with respect to the weld metal (WM) and heat affected zone (HAZ). Then, we investigated PCFs with respect to several regions of the weldment at various temperatures. Experimental values of PCFs were calculated and then compared against the predicted values according to the American Society for Testing and Materials (ASTM) standard. CTOD values of WM by SAW is found to be about three times higher than that of FCAW at −10 °C, and CTOD values calculated by the ASTM standard are approximately 30% lower than the CTOD according to British Standard (BS). In addition, the maximum of 40% discrepancy is observed in PCFs obtained between the experiment and the predicted values according to the ASTM standard. This may lead to too conservative fracture toughness estimation for the welded joints of API 2 W Gr. 50 steel when using PCF by ASTM. Based on the accurate estimated PCF values obtained from this study, it is believed that rational fracture design of offshore structures is possible.