We study the initial value problem of Einstein-Dirac system, and show the stability of Minkowski solution in the massless case with the use of generalized wave coordinates. Under a specific choice of the tetrad, we derive a quasilinear wave equation for components of the spinor field, where a null structure from the connection term is discovered, and we use this equation to study the behavior of the solution along the light cone when coupled with Einstein's equation. We also develop the estimate from the Dirac equation itself, which helps the estimate in the interior region.