Water-responsive shape-memory materials, especially cellulose nanofibers (CNF)-polymer composite materials, have been rapidly developed in recent years for designing new generation water-responsive sensors, actuators, biomedical devices, etc. However, achieving fast-responsivity is still a challenge. Herein, by simply incorporating CNF into a thermoplastic elastomer polyurethane (PU) matrix, we report a material, namely, PU/CNF nanocomposite, which has a good shape memory effect (SME) and fast responsivity. The effects of the CNF content on water absorption, shape memory behavior and mechanical properties of the composites are studied, and it can be found that when the CNF content reaches 30%, materials with good SME, such as high shape fixing and shape recovery ratio (higher than 90%) and fast responsivity (less than 1 min), can be obtained. The excellent SME can be ascribed to the combined effect of the good elastic recovery property of the PU matrix, high modulus of CNF and the rapid water uptake behavior of PU/CNF, based on which a rigid CNF percolation network in the elastomeric PU can be formed/destroyed by the desorption/absorption of water molecules repeatedly. Finally, based on the excellent rapid water-triggered shape memory performance, we also demonstrate some applications of the material, for example, as a "mechanical hand" to grasp solid objects in water and as a smart sealing film to build a controllable release system.