Device-to-device (D2D) communication enables us to spread information in the local area without infrastructure support. In this paper, we focus on information spreading in mobile wireless networks where all nodes move around. The source nodes deliver a given information packet to mobile users using D2D communication as an underlay to the cellular uplink. By stochastic geometry, we derive the average number of nodes that have successfully received a given information packet as a function of the transmission power and the number of transmissions. Based on these results, we formulate a redundancy minimization problem under the maximum transmission power and delay constraints. By solving the problem, we provide an optimal rule for the transmission power of the source node. andcopy; 2014 IEEE.