The error bounds of linear complementarity problems are studied. Firstly, the error bound theory of one kind of linear complementarity problems is presented by using a function of $M$-matrix whose main diagonal part is an identity matrix. Then, by transforming the model of linear complementarity problem, the error bound theory is generalized, and the error bound of linear complementarity problem whose system matrix is a general $M$-matrix is given. The error bound theory is verified and compared through low- and high-order examples. Numerical results show that the proposed error bound theory is effective and practical.