This paper deals with the consensus problems of multi-agent systems with nonlinear dynamics and sampled data information. The control input of each agent is based on the information of its neighbors at discrete sampling instants rather than the whole continuous process. An input delay approach is utilized to transform the sampling data into the time-varying delayed data. A novel time-dependent Lyapunov functional consisting of the continuous term and the discontinuous term is proposed. Tools like matrix theory, algebraic graph theory, relaxed matrix approach, and convex analysis technique are utilized to derive the sufficient conditions. The estimated upper bound of the sampling interval can be obtained by the proposed conditions. Then, the necessary and sufficient conditions for consensus in systems with linear dynamics are presented. It is shown that the consensus conditions depend on the parameters of the sampling interval, spectra of the Laplacian matrix, and coupling strength. The effectiveness of the proposed design method is demonstrated by the simulation examples.