MIMO detection technology plays an important role in MIMO communication system.For existing MIMO detection algorithm were for the AWGN wireless channel environment, the performance of these algorithms could significantly decline or even unable to work well when it encounter impulse noise in the power line channel.To suppress channel impulse noise in power line communication (PLC), a linear PLC MIMO detection algorithm based on a stable distribution is proposed in this paper.A linear detection algorithm, for example, ZF detection algorithm and MMSE detection algorithm, just needs to get the detection matrix.The proposed algorithm uses a stable distribution to model impulse noise in PLC channel.Under a stable distribution conditions, it should use Fractional Lower Order Statistics (FLOS) to deal with the signal, and here we use one kind of FLOC called fractional lower order correlation (FLOC).In the proposed algorithm, we calculate the optimal MIMO signal detection matrix by recursive least squares (RLS) method based on FLOC.It means that we use the RLS method to get the detection matrix, and use FLOC to make the cost function of RLS method.The simulation results show that the proposed algorithm has competitive performance to the existing method in an impulsive noise environment.