In this paper, a Euclidean direction search (EDS) based Laguerre adaptive filter for system identification is investigated. The EDS concept was first proposed by Xu and Bose as an alternative to the well-known recursive least squares (RLS) iterative solution. The convergence rate of the EDS algorithm is comparable to the RLS algorithm but is much more sensitive to the variations of the eigenvalue spread. The fast array Laguerre-RLS algorithm which was proposed by Ricardo Merched and Ali H. Sayed in (IEEE Trans. on Sig. Proc., 2001) is a very good method for adaptive system identification with long impulse response. Based on some analysis and computer simulations it is found that the EDS based Laguerre filter can achieve the fastest convergence rate with low filter order for adaptive system identification. Furthermore, it is demonstrated that the result has a comparable computational cost. Simulation results are presented in order to show the fastest convergence rate of this EDS based Laguerre filter.