Abstract. The aim of this study is to investigate through modelling how sputtering by impacting solar wind ions influences the lifetime of dust particles in the inner heliosphere near the Sun. We consider three typical dust materials, silicate, Fe0.4Mg0.6O, and carbon, and describe their sputtering yields based on atomic yields given by the Stopping and Range of Ions in Matter (SRIM) package. The influence of the solar wind is characterized by plasma density, solar wind speed, and solar wind composition, and we assume for these parameter values that are typical for fast solar wind, slow solar wind, and coronal mass ejection (CME) conditions to calculate the sputtering lifetimes of dust. To compare the sputtering lifetimes to typical sublimation lifetimes, we use temperature estimates based on Mie calculations and material vapour pressure derived with the MAGMA chemical equilibrium code. We also compare the sputtering lifetimes to the Poynting–Robertson lifetime and to the collision lifetime. We present a set of sputtering rates and lifetimes that can be used for estimating dust destruction in the fast and slow solar wind and during CME conditions. Our results can be applied to solid particles of a few nanometres and larger. The sputtering lifetimes increase linearly with the size of particles. We show that sputtering rates increase during CME conditions, primarily because of the high number densities of heavy ions in the CME plasma. The shortest sputtering lifetimes we find are for silicate, followed by Fe0.4Mg0.6O and carbon. In a comparison between sputtering and sublimation lifetimes we concentrate on the nanodust population. The comparison shows that sublimation is the faster destruction process within 0.1 AU for Fe0.4Mg0.6O, within 0.05 AU for carbon dust, and within 0.07 AU for silicate dust. The destruction by sputtering can play a role in the vicinity of the Sun. We discuss our findings in the context of recent F-corona intensity measurements onboard Parker Solar Probe.