Binaural speech intelligibility of individual listeners under realistic conditions was predicted using a model consisting of a gammatone filter bank, an independent equalization-cancellation (EC) process in each frequency band, a gammatone resynthesis, and the speech intelligibility index (SII). Hearing loss was simulated by adding uncorrelated masking noises (according to the pure-tone audiogram) to the ear channels. Speech intelligibility measurements were carried out with 8 normal-hearing and 15 hearing-impaired listeners, collecting speech reception threshold (SRT) data for three different room acoustic conditions (anechoic, office room, cafeteria hall) and eight directions of a single noise source (speech in front). Artificial EC processing errors derived from binaural masking level difference data using pure tones were incorporated into the model. Except for an adjustment of the SII-to-intelligibility mapping function, no model parameter was fitted to the SRT data of this study. The overall correlation coefficient between predicted and observed SRTs was 0.95. The dependence of the SRT of an individual listener on the noise direction and on room acoustics was predicted with a median correlation coefficient of 0.91. The effect of individual hearing impairment was predicted with a median correlation coefficient of 0.95. However, for mild hearing losses the release from masking was overestimated.