This technical note studies finite-time consensus problem for a team of networked nonlinear agents with unknown Lipschitz terms under communication constraints, where each agent has a limited sensing range. Because the induced interaction graph is typically state-dependent and dynamic, we propose a distributed nonlinear consensus algorithm that is capable of preserving the initial interaction patterns. By using tools from nonsmooth analysis, sufficient conditions are obtained such that finite-time consensus can be reached. An upper bound of the convergence time is derived via a two-step analysis. The validity of the theoretical result is shown by one simulation example.