This work considers the sequential hypothesis testing problem in the fully distributed sensor network. In specific, each sensor can observe samples over time, exchange information with adjacent sensors, and perform testing based on its own locally available decision statistic. Under such setting, we study the sequential probability ratio test based on the statistic that is obtained by running consensus algorithm. It is shown that, under certain regularity conditions on the data distribution and network topology, this distributed sequential test procedure yields the order-2 asymptotically optimal performance at all sensors.