The Gaia pixel-level data simulator GIBIS (Gaia Instrument and Basic Image Simulator, Babusiaux (2005)) provides detailed artificial data for all three instruments on-board the Gaia spacecraft. This data is used for the preparation of procedures required for the analysis of real Gaia data to come during the mission. Among the effects that strongly affect all Gaia data, that therefore have to be modelled with GIBIS, is charge transfer inefficiency (CTI). CTI, caused by radiation-induced microscopic defects in the CCD detectors, becomes manifest in a distortion of the line spread functions of observed objects, as well as in a loss of photo-generated charges inside the window allocated to each observed source. It affects the astrometric, photometric, and spectroscopic accuracy of the data. The CTI effects on a particular observation depend on observations done before, on CCD operations such as gate activity and charge injections, and on physical effects such as the sky background brightness and cosmic ray events in the detectors. In this paper, an approach for the simulation of CTI with GIBIS is presented and the influence of the sky background brightness and cosmic ray events of CTI is discussed in more detail.