Abstract: In Wireless Sensor Networks (WSNs), each sensor obtains data and have to communicate these data to a central node. Because sensors are battery powered they are highly energy constrained. Data aggregation can be used to combine data of several sensors into a single message, thus reducing the data traffic and the power consumption. This study has considered the problem of maximizing the time at which the first node with data aggregation in WSNs drains out of energy. It investigated optimal data aggregation routing for achieving the goal above. The problem is formulated as a linear programming problem. By solving the network lifetime optimization problem, the optimal solutions and the distributed implementation can be obtained that are based on the primal-dual decomposition. Simulation results indicate that the algorithm is superior to the existing methods.