This paper investigates privacy issues in distributed resource allocation over directed networks, where each agent holds a private cost function and optimizes its decision subject to a global coupling constraint through local interaction with other agents. Conventional methods for resource allocation over directed networks require all agents to transmit their original data to neighbors, which poses the risk of disclosing sensitive and private information. To address this issue, we propose an algorithm called differentially private dual gradient tracking (DP-DGT) for distributed resource allocation, which obfuscates the exchanged messages using independent Laplacian noise. Our algorithm ensures that the agents’ decisions converge to a neighborhood of the optimal solution almost surely. Furthermore, without the assumption of bounded gradients, we prove that the cumulative differential privacy loss under the proposed algorithm is finite even when the number of iterations goes to infinity. To the best of our knowledge, we are the first to simultaneously achieve these two goals in distributed resource allocation problems over directed networks. Finally, numerical simulations on economic dispatch problems within the IEEE 14-bus system illustrate the effectiveness of our proposed algorithm.