Aim The effectiveness of resistance training in improving cognitive function in older adults is well demonstrated. In particular, unconventional high‐speed resistance training can improve muscle power development. In the present study, the effectiveness of 12 weeks of elastic band‐based high‐speed power training (HSPT) was examined. Methods Participants were randomly assigned into a HSPT group (n = 14, age 75.0 ± 0.9 years), a low‐speed strength training (LSST) group (n = 9, age 76.0 ± 1.3 years) and a control group (CON; n = 7, age 78.0 ± 1.0 years). A 1‐h exercise program was provided twice a week for 12 weeks for the HSPT and LSST groups, and balance and tone exercises were carried out by the CON group. Results Significant increases in levels of cognitive function, physical function, and muscle strength were observed in both the HSPT and LSST groups. In cognitive function, significant improvements in the Mini‐Mental State Examination and Montreal Cognitive Assessment were seen in both the HSPT and LSST groups compared with the CON group. In physical functions, Short Physical Performance Battery scores were increased significantly in the HSPT and LSST groups compared with the CON group. In the 12 weeks of elastic band‐based training, the HSPT group showed greater improvements in older women with mild cognitive impairment than the LSST group, although both regimens were effective in improving cognitive function, physical function and muscle strength. Conclusions We conclude that elastic band‐based HSPT, as compared with LSST, is more efficient in helping older women with mild cognitive impairment to improve cognitive function, physical performance and muscle strength. Geriatr Gerontol Int 2017; 17: 765–772.