Abstract: In partial ordered Banach space deduced by normal cone, the existence of fixed points is discussed for a convex-power condensing operator which is increasing or decreasing. It is proved that when the convex-power condensing increasing operator is self-mapping in a cone interval, there exist the maximal and minimal fixed points and that when the convex-power condensing decreasing operator is cone-mapping, there exists a unique positive fixed point under certain conditions. In both cases, the iterative sequences converging to the fixed points are given.