A new speech intelligibility prediction model is presented which is based on the Computational Auditory Signal Processing and Perception model (CASP) of Jepsen, Ewert, and Dau [(2008). J. Acoust. Soc. Am. 124(1), 422–438]. The model combines a non-linear auditory-inspired preprocessing with a backend based on the cross-correlation between the clean and the degraded speech representations in the modulation envelope domain. Several speech degradation and speech enhancement algorithms were considered to study the ability of the model to predict data from normal-hearing listeners. Degradations of speech intelligibility due to additive noise, phase-jitter distortion, and single-channel noise reduction as well as improved speech intelligibility due to ideal binary mask processing are shown to be successfully accounted for by the model. Furthermore, the model reflects stimulus-level dependent effects of auditory perception, including audibility limitations at low levels and degraded speech intelligibility at high levels. Given its realistic non-linear auditory processing frontend, the speech-based computational auditory signal processing and perception model may provide a valuable computational framework for studying the effects of sensorineural hearing impairment on speech intelligibility.