To prevent data losses and service interruptions caused by natural disasters or human misconduct, we need to leverage periodic disaster backup among geographically distributed multiple datacenters. Previous works aimed at bandwidth allocation to achieve maximum network flow for every backup pair one by one or fair load distribution for backup datacenters respectively, without jointly optimizing the two problems to realize rapid and fair disaster backup. In this paper, we propose a new Receiving-Capacity-Constrained Rapid and Fair Disaster Backup strategy in the Software Defined Network scenarios. We formulate the disaster backup problem as a Receiving-Capacity-Constrained Capacitated Multi-Commodity Flow problem which is NP-complete. To solve the problem, we first construct a new effective Receiving-Capacity-Aware network model guaranteeing upper bound of bandwidth allocation to achieve fair load distribution for backup datacenters. And in this network model, we further propose a Bound-Aware Ant Colony Optimization algorithm satisfying backup flow constraint and lower bound constraint to achieve fast data transmission for backup pairs. Through extensive simulations, we demonstrate that our strategy has better performance with less total backup time and more fair load distribution than state-of-the-art algorithms.