Traditional federated learning (FL) methods often rely on fixed weighting for parameter aggregation, neglecting the mutual influence by others. Hence, their effectiveness in heterogeneous data contexts is limited. To address this problem, we propose an influence-oriented federated learning framework, namely FedC^2I, which quantitatively measures Client-level and Class-level Influence to realize adaptive parameter aggregation for each client. Our core idea is to explicitly model the inter-client influence within an FL system via the well-crafted influence vector and influence matrix. The influence vector quantifies client-level influence, enables clients to selectively acquire knowledge from others, and guides the aggregation of feature representation layers. Meanwhile, the influence matrix captures class-level influence in a more fine-grained manner to achieve personalized classifier aggregation. We evaluate the performance of FedC^2I against existing federated learning methods under non-IID settings and the results demonstrate the superiority of our method.