In this article, we study the propagation of scalar fields in the gravitational background of a spherically symmetric, electrically charged, regular-de Sitter black holes in higher dimensions. We carry out a thorough investigation of the grey body factors, by deriving analytical expressions for both minimally and non-minimally coupled scalar fields. Then we study the profile of grey body factors in terms of particle properties, namely the angular momentum quantum number and the non-minimal coupling constant, and the spacetime properties, namely the dimension, the cosmological constant and the non-linear charge parameter. We then derive the Hawking radiation spectra for a higher-dimensional electrically charged regular-de Sitter black hole. We find that the non-minimal coupling may suppress the greybody factor and the non-linear charge parameter may enhance it, but they both suppress the energy emission rate of Hawking radiation.