Abstract: By introducing the relaxation strategies to the general implicit fixed-point equation, a general relaxation two-sweep modulus-based matrix splitting iteration method is established for linear complementarity problems, which extends the existing relaxation two-sweep modulus-based matrix splitting iteration method to more general cases. Based on some special properties of H₊-matrices, the convergence analyses are given when the system matrices are H₊-matrices. Numerical results verify that the new general methods derived from the proposed method are superior to the existing general modulus-based matrix splitting iteration methods and two-sweep modulus-based matrix splitting iteration methods in terms of the number of iteration steps and CPU time.