This paper addresses the parameter identification problem for multi-input single-output Hammerstein-Wiener systems with errors-in-variables (Error-In-Variables, EIV), where both input and output measurements are corrupted by additive white noise. A bias-compensated least squares (Least Square, LS) algorithm is proposed to achieve consistent estimation of the nonlinear EIV MISO Hammerstein-Wiener model. First, the inherent bias mechanism in conventional LS estimation is analytically investigated using matrix reconstruction theory, yielding an explicit bias expression. Second, a multi-dimensional search algorithm is developed to accurately estimate unknown noise variances, which is crucial for practical industrial applications. Furthermore, a bias elimination scheme based on higher-order moment theory of stationary stochastic processes is introduced to ensure consistent parameter estimation. Finally, Monte Carlo simulation experiments under various noise levels demonstrate that the proposed Bias-Correction Least Squares(BCLS) algorithm achieves significant improvements over the conventional least-squares method and other comparative approaches in both parameter estimation accuracy and output fitting performance, thereby corroborating the effectiveness and robustness of the proposed algorithm.