Nanocellulose network in the form of cellulose nanopaper is an important material structure and its time-dependent mechanical response is crucial in many of its potential applications. In this work, we report the influences of grammage and strain rate on the tensile response of bacterial cellulose (BC) nanopaper. BC nanopaper with grammages of 20, 40, 60 and 80 g m−2 were tested in tension at strain rates ranging from 0.1% s−1 to 50% s−1. At strain rates ≤ 2.5% s−1, both the tensile modulus and strength of the BC nanopapers stayed constant at ~ 14 GPa and ~ 120 MPa, respectively. At higher strain rates of 25% s−1 and 50% s−1 however, the tensile properties of the BC nanopapers decreased significantly. This observed anomalous tensile response of BC nanopaper is attributed to inertial effect, in which some of the curled BC nanofibres within the nanopaper structure do not have enough time to uncurl before failure at such high strain rates. Our measurements further showed that BC nanopaper showed little deformation under creep, with a secondary creep rate of only ~ 10–6 s−1. This stems from the highly crystalline nature of BC, as well as the large number of contact or physical crosslinking points between adjacent BC nanofibres, further reducing the mobility of the BC nanofibres in the nanopaper structure.