The self-consistent simulation of the edge plasma is crucial for exploring the edge plasma solution compatible with high-performance plasma. While self-consistent edge plasma simulation is subject to the large gap between the turbulence and transport time scales, the coupling simulation of the turbulence and transport code is considered a reasonable way with both solid physics foundations and tolerable computational consumption. In this work, for the purpose of implementing the self-consistent turbulence-transport coupling simulation of the edge plasma automatically and efficiently, a simulation framework called edge plasma coupling simulation (EPCS) is developed based on Python. EPCS consists of various components to provide the interfaces for the specified turbulence and transport codes (BOUT++ and SOLPS-ITER at the present stage), the data transfer interfaces between the turbulence and transport code, the code running drivers and the function for configuration of the specified coupling simulation workflow. The inverse bilinear interpolation/bivariate spline interpolation under the flux-surface-aligned coordinate system is used to realize the accurate data transfer between different codes, and the breadth-first search algorithm is adopted to accelerate the interpolation process. A quasi-steady state identification method based on the coefficient of variation is developed to speed up the coupling simulation by terminating the turbulence simulation in time. Based on the components in EPCS, a steady-state coupling simulation workflow is developed, where the edge plasma is simulated by iterations of turbulence and transport codes. The steady-state coupling simulation workflow is validated by comparing the converged plasma profiles with EAST experiments (edge-localized-mode-free stage) at both upstream and divertor target, which implies the capability and flexibility of EPCS for the self-consistent simulation of the edge plasma under steady state.