Abstract: The first-order absorbing boundary condition is extended to improve accuracy both on the free field boundary and the input wave boundary. The computer program of this absorbing boundary condition is based on finite element method. The input wave is introduced into Higdon’s boundary condition by using least-squares method, while the parameters in Higdon’s operator are estimated by the nodal strain and velocity fields inside absorbing boundary. As a result, the absorbing boundary condition is updated automatically. The velocity boundary condition and the force boundary condition are proposed to absorb reflected wave both on the free field boundary and the input wave boundary. Numerical examples show that the proposed boundary conditions have much higher accuracy compared with the conventional artificial boundary conditions.