Classical barium stars are red giants that receive from their evolved binary companions material exposed to the slow neutron-capture nucleosynthesis, i.e. the s-process. Such a mechanism is expected to have taken place in the interiors of Thermally-Pulsing Asymptotic Giant Branch (TP-AGB) stars. As post-interacting binaries, barium stars figure as powerful tracers of the s-process nucleosynthesis, evolution of binary systems, and mechanisms of mass transfer. The present study is the fourth in a series of high-resolution spectroscopic analyses on a sample of 180 barium stars, for which we report tungsten (W, Z = 74) abundances. The abundances were derived from synthetic spectrum computations of the W I absorption features at 4843.8 and 5224.7 Å. We were able to extract abundances for 94 stars; the measured [W/Fe] ratios range from ∼0.0 to 2.0 dex, increasing with decreasing metallicity. We noticed that in the plane [W/Fe] versus [s/Fe], barium stars follow the same trend observed in post-AGB stars. The observational data were also compared with predictions of the FRUITY and Monash AGB nucleosynthesis models. These expect values between −0.20 and +0.10 dex for the [W/hs] ratios, whereas a larger spread is observed in the program stars, with [W/hs] ranging from −0.40 to +0.60 dex. The stars with high [W/hs] ratios may represent evidence for the operation of the intermediate neuron-capture process at metallicities close to solar.