The network lifetime problem of broadcast for mobile ad hoc networks has always been an interesting and hot research topic.The  existing research has proved that the broadcast algorithm based on the minimum spanning tree can optimally solve the network lifetime problem. However,these research activities are all based on static network topology,which is not suitable for some practical scenarios with changeable network topologies,such as the military communications. Therefore,for these scenarios,this paper proposes a maximum network lifetime broadcast algorithm called LONG for mobile ad hoc networks. This broadcast algorithm is based on motion prediction and the basic idea of the minimum spanning tree algorithm,and is implemented using the Fibonacci heap.A theoretical analysis shows LONG achieves the maximum network lifetime,and its time complexity is O(n2),where  n  denotes the number of nodes in the networks. Finally,the results of the extensive simulation implemented by NS2 show that,the packet delivery ratio and the  network lifetime of LONG are better than those of other broadcast algorithms.