In contrast to Brownian transport, the active motility of microbes, cells, animals and even human soften follows another random process known as truncated Levy walk(1,2). These stochastic motions are characterized by clustered small steps and intermittent longer jumps that often extend towards the size of the entire system. As there are repeated suggestions, although disagreement, that Levy walks have functional advantages over Brownian motion in random searching and transport kinetics(3-8), their intentional engineering into active materials could be useful. Here, we show experimentally in the classic active matter system of intracellular tracking(9-15) that Brownian-like steps self-organize into truncated Levy walks through an apparent time-independent positive feedback such that directional persistence increases with the distance travelled persistently. A molecular model that allows the maximum output of the active propelling forces to fluctuate slowly fits the experiments quantitatively. Our findings offer design principles for programming effcient transport in active materials.