Robust detection of known signal in non-Gaussian Markov noise is considered under the assumptions that only marginal distribution class and dependent coefficient of noise samples are given，and the noise sequences can be expressed as a first-order AR process: n_i=ρn_i-1+Y_i (i=1，2，… N)，where {Y_i} is i.i.d. sequence. If ρ is smaller, the memory and memory less robust detectors are respectively derived by minimax of the first-order and the second-order approximation of detection efficacy to ρ.