In this work we address the full state finite-time distributed consensus control problem for high-order multi-agent systems (MAS) under directed communication topology. Existing protocols for finite time consensus of MAS are normally based on the signum function or fractional power state feedback, and the finite convergence time is contingent upon the initial conditions and other design parameters. In this paper, by using regular local state feedback only, we present a distributed and smooth finite time control scheme to achieve leader follower consensus under the communication topology containing a directed spanning tree. The proposed control consists of a finite time observer and a finite time compensator. The salient feature of the proposed method is that both the finite time intervals for observing leader states and for reaching consensus are independent of initial conditions and any other design parameters, thus can be explicitly pre-specified, Leader-following problem of MAS with both single and multiple leaders are studied. (C) 2017 Elsevier Ltd. All rights reserved.