<p>Traditional gradient descent-based parameter estimation methods (e.g., the least mean squares method) may induce significant estimation bias when they are directly applied to the errors-in-variables system. This paper concerns the unbiased gradient estimation problem of the errors-in-variables time-delay system. The time-delay system is transformed into an augmented identification model by using redundant rule. To compensate the bias caused by the input and output noise, multiple-bias compensation terms are introduced into the gradient scheme based on the unbiasedness criterion and a multiple-bias compensations-based gradient estimation method is presented. Moreover, the relationship among system parameters, noise variances and the cost function is explicitly expressed so that the system parameters, the noise variances and the time-delay can be simultaneously estimated. The simulations verify the effectiveness of the proposed method.</p>