This paper proposes a new method to discuss the perturbation problem of the LR fuzzy linear systems by an embedding method. By solving the perturbation equation of the original fuzzy linear systems, the respective relative error bounds are analyzed and obtained: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged; and (c) both the coefficient matrix and the right hand side are perturbed. Some numerical examples are given to illustrated our proposed method. The results enrich the computation theories of fuzzy linear systems.