Thin films of multi-walled carbon nanotubes forming random networks were produced by vacuum filtration method, and their broadband electromagnetic radiation transmittance spectra are presented. Thickness of the nanotube films was between 100 nm and 1 lm, and the transmission properties are demonstrated for the wavelength range from 300 nm to 400 lm. It is observed that transmittance is an increasing function of a radiation wavelength, and for the thickest films it almost saturates above 1 lm wavelength. To explain the experimental results in the ultraviolet-near infrared range, we employed effective medium theory (in the form of symmetric Bruggeman model) correlating properties of multi-walled carbon nanotubes with the effective dielectric function of a nanotube network. The optical properties of a single multi-walled carbon nanotube that were used for calculations were based on ordinary and extraordinary dielectric functions of bulk graphite. The proposed theoretical model has been successfully fitted to the experimental results. It has been also found that despite the fact that radiation undergoes multiple internal reflections at the film interfaces, the transmittance-thickness relation can be still described by exponential decay.