In this paper, the J-R curves of two cracks (A508 HAZ crack 2 and A508/Alloy52Mb interface crack 3) located at the weakest region in an Alloy52M dissimilar metal welded joint (DMWJ) for connecting pipe-nozzle of nuclear pressure vessel have been measured by using single edge-notched bend (SENB) specimens with different crack depths a/W (different constraint). Based on the modified T-stress constraint parameter τ*, the equations of constraint-dependent J-R curves for the crack 2 and crack 3 were obtained. The predicted J-R curves using different constraint equations derived from the three pairs of crack growth amount all agree with the experimental J-R curves. The results show that the modified T-stress approach for obtaining constraint-dependent J-R curves of homogeneous materials can also be used for the DMWJs with highly heterogeneous mechanical properties (local strength mismatches) in nuclear power plants. The use of the constraint-dependent J-R curves may increase the accuracy of structural integrity design and assessment for the DMWJs of nuclear pressure vessels.