We propose an objective intelligibility measure (OIM), called the Gammachirp Envelope Similarity Index (GESI), that can predict speech intelligibility (SI) in older adults. GESI is a bottom-up model based on psychoacoustic knowledge from the peripheral to the central auditory system and requires no training data. It computes the single SI metric using the gammachirp filterbank (GCFB), the modulation filterbank, and the extended cosine similarity measure. It takes into account not only the hearing level represented in the audiogram, but also the temporal processing characteristics captured by the temporal modulation transfer function (TMTF). To evaluate performance, SI experiments were conducted with older adults of various hearing levels using speech-in-noise with ideal speech enhancement on familiarity-controlled words. The prediction performance was compared with HASPIw2, which was developed for keyword SI prediction. The results showed that GESI predicted the subjective SI scores more accurately than HASPIw2. The effect of introducing TMTF into the GESI algorithm was not significant, indicating that more research is needed to know how to introduce temporal response characteristics into the OIM.