Due to safety constraints and unstable open-loop dynamics, system identification of many real-world processes often requires gathering data from closed-loop experiments. In this paper, we present a bias-correction scheme for closed-loop identification of Linear Parameter-Varying Input Output (LPV-IO) models, which aims at correcting the bias caused by the correlation between the input signal exciting the process and output noise. The proposed identification algorithm provides a consistent estimate of the open-loop model parameters when both the output signal and the scheduling variable are corrupted by measurement noise. The effectiveness of the proposed methodology is tested in two simulation case studies. (C) 2017 Elsevier Ltd. All rights reserved.