Federated learning(FL) is an emerging distributed learning paradigm with default client privacy because clients can keep sensitive data on their devices and only share local training parameter updates with the federated server. However, recent studies reveal that gradient leakages in FL may compromise the privacy of client training data. This paper presents a gradient leakage resilient approach to privacy-preserving federated learning with per training example-based client differential privacy, coined as Fed-CDP. It makes three original contributions. First, we identify three types of client gradient leakage threats in federated learning even with encrypted client-server communications. We articulate when and why the conventional server coordinated differential privacy approach, coined as Fed-SDP, is insufficient to protect the privacy of the training data. Second, we introduce Fed-CDP, the per example-based client differential privacy algorithm, and provide a formal analysis of Fed-CDP with the $(ε, δ)$ differential privacy guarantee, and a formal comparison between Fed-CDP and Fed-SDP in terms of privacy accounting. Third, we formally analyze the privacy-utility trade-off for providing differential privacy guarantee by Fed-CDP and present a dynamic decay noise-injection policy to further improve the accuracy and resiliency of Fed-CDP. We evaluate and compare Fed-CDP and Fed-CDP(decay) with Fed-SDP in terms of differential privacy guarantee and gradient leakage resilience over five benchmark datasets. The results show that the Fed-CDP approach outperforms conventional Fed-SDP in terms of resilience to client gradient leakages while offering competitive accuracy performance in federated learning.