Impact of plasma core profiles on magnetohydrodynamics (MHD) stability at tokamak edge pedestal is investigated numerically to extend an operation regime for small amplitude grassy edge localized mode (ELM). With the hypotheses that pedestal pressure profile can be predicted with the EPED1 model and the trigger of grassy ELM is an ideal ballooning mode, the impacts of plasma poloidal beta and plasma internal inductance on edge MHD stability are investigated, the parameters of which are related to plasma core profiles and are important parameters for grassy ELMy H-modes in JET quasi-double null plasma. The numerical results indicate that a ballooning mode can be destabilized by decreasing poloidal beta and/or internal inductance. In contrast, it is confirmed that pedestal density, which is also an important parameter for realizing grassy ELMy H-mode, can stabilize a ballooning mode. In combination with these trends, it is possible to relax the necessary conditions for grassy ELMy H-mode by adjusting the parameters carefully, though this relaxation destabilizes type-I ELM more easily due to the increase in edge current density.