The CALIOPE air quality modelling system has been used to diagnose ground level O3 concentration for the year 2004, over the Iberian Peninsula. We investigate the improvement in the simulation of daily O3 maximum by the use of a post-processing such as the Kalman filter bias-adjustment technique. The Kalman filter bias-adjustment technique is a recursive algorithm to optimally estimate bias-adjustment terms from previous measurements and model results. The bias-adjustment technique improved the simulation of daily O3 maximum for the entire year and the all the stations considered over the whole domain. The corrected simulation presents improvements in statistical indicators such as correlation, root mean square error, mean bias, and gross error. After the post-processing the exceedances of O3 concentration limits, as established by the European Directive 2008/50/CE, are better reproduced and the uncertainty of the modelling system, as established by the European Directive 2008/50/CE, is reduced from 20% to 7.5%. Such uncertainty in the model results is under the established EU limit of the 50%. Significant improvements in the O3 timing and amplitude of the daily cycle are also observed after the post-processing. The systematic improvements in the O3 maximum simulations suggest that the Kalman filter post-processing method is a suitable technique to reproduce accurate estimate of ground-level O3 concentration. With this study we evince that the adjusted O3 concentrations obtained after the post-process of the results from the CALIOPE system are a reliable means for real near time O3 forecasts.