Engineering critical assessment (ECA) is an evaluation procedure for structures with flaws and has been widely applied for assessing pipeline integrity. The standards for structural integrity assessment, including BS 7910, involve stress-based ECA, and they are known to produce overly conservative results. Therefore, strain-based ECA has been recently developed as an alternative approach. One of the effective methods for improving the accuracy of strain-based ECA is the reference strain method. However, only a limited number of studies have applied this method to welded pipelines. Therefore, a numerical analysis based on strain-based ECA was performed for girth-welded joints with a circumferentially oriented internal surface crack. Particular attention was given to the strength mismatch effects. The equivalent stress–strain curve in BS7910 was used to reflect the strength mismatch effects in the reference strain. The results of the proposed method were validated with the results of a finite element analysis (FEA) in terms of the J-integral. Previous methods and the proposed method exhibit a reasonable correlation of the J-integral in the case of over-matching (OM). In the under-matching (UM) cases, while the previous procedures tended to underestimate or excessively overestimate the elastic-plastic energy release rate in comparison with the FEA, the proposed method evaluated the J-integral of pipelines with sufficient accuracy.