This paper introduces a new efficient algorithm, called MXL_3, for computing Gröbner bases of zero-dimensional ideals. The MXL_3 is based on XL algorithm, mutant strategy, and a new sufficient condition for a set of polynomials to be a Gröbner basis. We present experimental results comparing the behavior of MXL_3 to F_4 on HFE and random generated instances of the MQ problem. In both cases the first implementation of the MXL_3 algorithm succeeds faster and uses less memory than Magma’s implementation of F_4.