Abstract: The asteroid is of great significance for studying the formation of planets, the origin of life on the Earth, the defense against the collision of asteroids to the Earth and the mining on asteroids. Due to the insufficient capacity of the existing propulsion technology, the velocity increment needed to optimize the asteroid capture is the key for a successful capture mission. This paper reviews the capture orbit optimization method for asteroid and the extended capture period with the impulse thrust and lowthrust propulsions, including the strategy to capture asteroids by the gravity assisted and resonant orbital techniques, the continuous low thrust and temporary asteroid capture, and the scheme of extending the capture period.