In order to add the kinds of the sort algorithms which have the complexity of O(n²) and then serve teaching and daily application better, the paper proposes a new sort algorithm-bidirectional selection sort algorithm. Through mathematical method that the time complexity of the new algorithm is O(n²) and its space complexity is O(1). It is known by empirical method that the running time of the new algorithm is averagely 27 percent of bubble sort, and 62 percent of simple selection sort and 88 percent direct insertion sort in same condition.