Sensorineural hearing loss occurs due to damage to the inner and outer hair cells of the peripheral auditory system. Hearing loss can cause decreases in audibility, dynamic range, frequency and temporal resolution of the auditory system, and all of these effects are known to affect speech intelligibility. In this study, a new reference-free speech intelligibility metric is proposed using 2-D neurograms constructed from the output of a computational model of the auditory periphery. The responses of the auditory-nerve fibers with a wide range of characteristic frequencies were simulated to construct neurograms. The features of the neurograms were extracted using third-order statistics referred to as bispectrum. The phase coupling of neurogram bispectrum provides a unique insight for the presence (or deficit) of supra-threshold nonlinearities beyond audibility for listeners with normal hearing (or hearing loss). The speech intelligibility scores predicted by the proposed method were compared to the behavioral scores for listeners with normal hearing and hearing loss both in quiet and under noisy background conditions. The results were also compared to the performance of some existing methods. The predicted results showed a good fit with a small error suggesting that the subjective scores can be estimated reliably using the proposed neural-response-based metric. The proposed metric also had a wide dynamic range, and the predicted scores were well-separated as a function of hearing loss. The proposed metric successfully captures the effects of hearing loss and supra-threshold nonlinearities on speech intelligibility. This metric could be applied to evaluate the performance of various speech-processing algorithms designed for hearing aids and cochlear implants.