The errors-in-variables (EIV) model is widely used in linear systems where both input and output signals are contaminated with noise. For the parameter estimation in the EIV model, the adaptive filtering algorithm using total least squares (TLS) approach has shown better performance than classical least squares (LS) approach. However, the TLS approach which is based on minimizing the mean squared total error may be irrational in the presence of impulsive noise. To address this problem, a novel robust adaptive algorithm, named as the total least mean M-estimate (TLMM) algorithm, is proposed in this brief, which combines the advantages of TLS approach and M-estimate function. In addition, to further improve the performance of the TLMM algorithm, its variable step-size (VSS) version has been developed. Moreover, we carry out the local stability analysis and the computational complexity analysis. Simulation results show that the proposed algorithms outperform some well-known algorithms.