The viscoelasticity of boron nitride nanosheet (BNNS) aerogel has been observed and investigated. It is found that the BNNS aerogel has a high damping ratio (0.2), while it exhibits lightweight and negligible temperature dependence below 180 °C. The creep behavior of the BNNS aerogel markedly demonstrates its strain dependence on stress magnitude and temperature, and can be well simulated by the classical models.