Federated Learning (FL) is a distributed machine learning technique that allows model training among multiple devices or organizations by sharing training parameters instead of raw data. However, adversaries can still infer individual information through inference attacks (e.g. differential attacks) on these training parameters. As a result, Differential Privacy (DP) has been widely used in FL to prevent such attacks. We consider differentially private federated learning in a resource-constrained scenario, where both privacy budget and communication rounds are constrained. By theoretically analyzing the convergence, we can find the optimal number of local DPSGD iterations for clients between any two sequential global updates. Based on this, we design an algorithm of Differentially Private Federated Learning with Adaptive Local Iterations (ALI-DPFL). We experiment our algorithm on the MNIST, FashionMNIST and Cifar10 datasets, and demonstrate significantly better performances than previous work in the resource-constraint scenario. Code is available at https://github.com/cheng-t/ALI-DPFL.