Via three-dimensional particle-in-cell simulations, the self-mode-transition of a laser-driven electron acceleration from laser wakefield to plasma-wakefield acceleration is studied. In laser wakefield accelerator (LWFA) mode, an intense laser pulse creates a large amplitude wakefield resulting in high-energy electrons. Along with the laser pulse depletion, the electron bunch accelerated in the LWFA mode drives a plasma wakefield. Then, after the plasma wakefield accelerator mode is established, electrons are trapped and accelerated in the plasma wakefield. The mode transition process and the characteristics of the accelerated electron beam are presented.