A distributed local adaptive transmit power assignment (LA-TPA) strategy was proposed to construct a topology with better performance according to the environment and application scenario and prolong the network lifetime.It takes the path loss exponent and the energy control coefficient into consideration with the aim to accentuate the minimum covering district of each node more accurately and precisely according to various network application scenarios.Besides,a self-healing scheme that enhances the robustness of the network was provided.It makes the topology tolerate more dead nodes than existing algorithms.Simulation was done under OMNeT++ platform and the results show that the LA-TPA strategy is more effective in constructing a well-performance network topology based on various application scenarios and can prolong the network lifetime significantly.