The success probability of the Grover quantum search algorithm decreases quickly when the fraction of target items exceeds 1/4,where the phase plays a significant role.Therefore,we use multiple phases to complement each other.We obtain three useful properties and an important theorem of the success probability and design a systematic solution of the optimal phases for an arbitrary number of phases.Based on these results,we finally propose a multi-phase quantum search algorithm whose success probability rises with the increase of the number of phases with just a single iteration,and it tends to be 100％ when the fraction of target items is over a lower limit.