Device-to-device (D2D) discovery is a key enabler of D2D communications for the direct exchange of local area traffic between proximity users (UEs) to improve spectral efficiency. The direct D2D discovery relies on the capabilities of the D2D UEs to autonomously indicate their presence to proximity D2D UEs. Despite its potential of reducing energy and signaling burden, the direct D2D discovery has not drawn adequate attention. In this paper, we propose a direct D2D discovery scheme based on the random backoff procedure, where D2D UEs randomly choose a backoff interval and retransmit a beacon. Compared with existing schemes, the performance of the proposed scheme can be significantly enhanced in terms of the discovery probability and the discovery delay. Several useful guidelines for its design are proposed based on our analysis. Finally, numerical results provide valuable insights on the performance tradeoff inherent to the proposed D2D discovery scheme.