In this paper, we propose a novel Backoff scheme, dubbed Padovan Backoff Algorithm (PBA), to improve the efficiency of IEEE 802.11 MAC protocol when operating in DCF mode. PBA will enable significant reduction of the number of collisions when more than one node try to access the shared wireless medium concurrently, leading to an enhanced network performance. The Binary Exponential Backoff (BEB) scheme used in IEEE 802.11 has been proven to not be the optimal backoff algorithm for MANETs. This is mainly due to the exponential increase of the Contention Window (CW) size when a collision occurs, which results in picking the random backoff timer from a large interval that may lead to a longer waiting time before the node tries to retransmit again. Therefore, this waiting time for the idle medium could be important, especially in dense networks where consecutive collisions are more likely to happen, and thus causes a severe degradation of the network performance. To overcome the above issue, PBA employs a different scheme that reduces the size of CW as compared to BEB, thanks to the Padovan sequence. The obtained simulation results reveal that the PBA allows more efficient network resources utilization and outperforms the legacy BEB scheme in different scenarios.