This study investigates the crack growth behavior due to primary water stress corrosion cracking (PWSCC) in the dissimilar metal butt weld of a reactor piping using Alloy 82/182. First, detailed finite element stress analyses were performed to predict the stress distribution of the dissimilar metal butt weld in which the hydrostatic and the normal operating loads as well as the weld residual stresses were considered to evaluate the stress redistribution due to mechanical loadings. Based on the stress distributions along the wall thickness of the dissimilar metal butt weld, the crack growth behavior of the postulated axial and circumferential cracks were predicted, from which the crack growth diagram due to PWSCC was proposed. The present results can be applied to predict the crack growth rate in the dissimilar metal butt weld of reactor piping due to PWSCC.