The effective viscosity coefficient of rarefied gas nanosuspensions is calculated by means of Boltzmann kinetic theory. The dependence of this coefficient on the radius of nanoparticles, their concentration, and temperature of a carrier gas is investigated. It is shown that the viscosity of gas nanosuspensions depending on the nanoparticle concentration and size can both increase and decrease compared with the viscosity of the carrier gas. The results obtained are compared with the data for binary mixtures of rarefied gases.