The fracture phase-field method, based on the variational description of Griffith theory, has shown promising capabilities in simulating brittle fracture. However, general cohesive fracture phase-field theory remains far from mature. Recently, an integral transform phase-field model has been proposed to derive the phase-field model from the cohesion law in a more unified form. Theoretically, the phase-field model based on the aforementioned integral transform can realize arbitrary cohesion laws. Yet, practical difficulties may arise when dealing with complex softening laws—particularly those featuring inflection points or non-integrable forms. This paper, starting from the mathematical theory of integral transform phase-field, rigorously derives expressions from simple to complex cohesion curves. As the complexity increases, different numerical methods are used to approximate the cohesion law. The numerical singularity of the theoretical model can be solved using staggered iterations through a simple Maclaurin expansion. Finally, the studied cohesion curves are verified with analytical solutions. The method proposed in this paper can be used to reproduce complex cohesion laws in practical engineering applications.