Filtration of aerosol particles using composites of nano- and microsized fibrous structures is a promising method of effective separation of nanoparticles from gases. The multiscale physical system describing the flow pattern and particles deposition in it requires other than a continuous approach for the process analysis. The lattice-Boltzmann method was used for the calculation of deposition efficiency on nanosized particles for the system consisting of two nano- and microsized fibers. The proposed method allows to calculate the deposition efficiency of nanoparticles on both fibers for a very wide range of Knudsen numbers in the case of each nanofiber considering molecular, slip, and continuous flow patterns. The nanofiber is a significant attractor for collecting particles as an element of multiscale fibers of the filtration composite. The results of particle deposition efficiency calculated for the microfiber, using proposed method, are similar to those obtained from the classical continuum approach ( Filippova and Hanel 1997 Filippova, O. and Hanel, D. 1997. Lattice-Boltzmann Simulation of Gas-Particle Flow in Filters. Computers and Fluids, 26: 697–712. [Crossref], [Web of Science ®] [Google Scholar] ; Przekop et al. 2003 Przekop, R. , Moskal, A. and Gradoń, L. 2003. Lattice-Boltzmann Approach for Description of the Structure of Deposited Particulate Matter in Fibrous Filters. J. Aerosol Sci., 34: 133–147. [Crossref], [Web of Science ®] [Google Scholar] ). The proposed model was extended to calculate the performance of bilayer filter structures consisting of a nanofibrous front layer and a microfibrous backing layer of the filter. Filtration efficiency, pressure drop and quality factors for uniform and non-uniform distributions of nanofibers in the front filter layer were calculated for a wide range of Knudsen and Peclet numbers.