Based on Eulerian ADER scheme,we build a 1D,one-step,conservative,high-order accurate,Lagrangian ADER(LADER) scheme.Main procedures of r-th order LADER scheme include:Deducing integral form of the equations in Lagrangian framework from Euler equations,using WENO reconstruction method to reconstruct conserved variables and their spatial derivatives up to (r-1)-th order on interface of mesh with high-order accuracy,evaluating Godunov values of conserved variables and their space derivatives in Lagrangian framework,computing time material derivatives of conserved variables,approximating time-integral average of physical flux function with high-order accuracy at last.Simulation of smooth regions shows that LADER scheme achieves desired accuracy and examples of discontinuous regions show the scheme is essentially non-oscillatory near discontinuities.