In this paper, finite-time adaptive consensus problem is investigated for first-order multiagent systems with unknown nonlinear dynamics. Linearly parameterized method is introduced to model unknown nonlinear dynamics of the systems. By only utilizing the local relative position state information between each agent and its neighbors, decentralized finite-time adaptive consensus algorithms are presented with directed fixed and switching network topologies which satisfy detailed balance condition. Based on classical Lyapunov analysis techniques, both finite-time stability and finite-time parameter convergence are guaranteed by making use of the proposed control algorithms. Finally, the results in Simulations part are presented to validate our main results.