Contemporarily, the collider plays a vital role in research and analysis for high energy physics, particle physics and astrophysics. However, conventional colliders usually need a large budget to operate as well as cover a large area for displacing the facility. With the rapid development of the laser techniques, the laser-plasma accelerator paves a path to accelerate particles in a compact way. On this basis, this paper will analyze the feasibility and recent progress for electron-positron collider realization via the concept of the laser-plasma acceleration. To be specific, the principles behind it will be analyzed initially. To be specific, an intense electromagnetic could make the plasma oscillated due to the pondermotive force, and the electron field created by the oscillation of the plasma could accelerate electrons to high energy. In addition, the possibility of applying laser plasma acceleration in to electron-positron collider is examined. These results shed light on guiding the further exploration of future electron-positron collider.