•Pool-rewarding is incorporated into N-person snowdrift game to reveal its influence on cooperation.•In well-mixed population, increasing rewarding synergy factor generates oscillating periodic phase.•In structured population, rewarders tend to dominate at moderate rewarding synergy factor for small cost. We extend the N-person snowdrift game (NSG) to incorporate the effects of pool rewarding. An individual who chooses to reward pays a certain cost to provide additional benefits to cooperative behaviors. Thus, rewarding can be considered as a second-order altruistic behavior. But rewarders are actually indirectly protected by defectors as system dynamics evolves. Both the well-mixed version of NSG and the spatial game have been investigated. For well-mixed population, increasing the synergy factor of rewarding r2 facilitates the formation of an oscillating state, while the increment of NSG synergy factor r1 promotes the transition from the stable closed orbit to a fixed state of the system. For structured population, dynamic diversity is dramatically enriched. Especially, the existence of rewarders makes “cooperation monopolization”(the domination of cooperators or rewarders) emerge under feasible parameters. Moreover, for small reward cost, the system dynamics can converge to the absorbing state of rewarding even when the r2 value is low. Larger reward cost, however, is not conducive to the prevalence of rewarding, but dramatically promotes second-order free-riding. Based on this study, we hope to provide guidance for the future research of positive incentives in NSG.