The problem of a Griffith crack interacting with a circular inclusion by considering a nearby edge dislocation is studied in this work. The cracks are modelled by distributed dislocation method, which results in a set of singular integral equations with Cauchy kernels and can be solved numerically. Irwin plastic zone correction method is employed to improve the fracture analysis based on the linear elastic fracture mechanics. The von Mises yield criterion is used to differentiate the elastic and plastic deformation at the crack tips. As the first time to analyze the elastic-plastic fracture behavior of a Griffith crack interacting with a nearby edge dislocation and circular inclusion, we emphasized the influence of the inclusion/matrix material properties, dislocation position parameters and burgers vectors of the edge dislocation. It is found that the normalized stress intensity factor, plastic zone size and CTOD are very sensitive to the change of edge dislocation position against the target crack tip. When the distance between the edge dislocation and crack tip are fixed and only the angle varies, the maximum value of the normalized stress intensity factor can be achieve at . When the edge dislocation is located along the crack line or vertical to the crack line, the normalized SIF, PZS and CTOD are smaller than the rest. The mixed-mode loading condition also contribute to the SIF, PZS and CTOD a lot and also influence the effect of other parameters.