Filter-feeding gelatinous macrozooplankton (FFGM), namely salps, pyrosomes and doliolids, are increasingly recognized as an essential component of the marine ecosystem. Unlike crustacean zooplankton (e.g., copepods) that feed on preys that are an order of magnitude smaller, filter-feeding allows FFGM to have access to a wider range of organisms, with predator over prey ratios as high as 10$^5$:1. In addition, most FFGM produce carcasses and/or fecal pellets that sink 10 times faster than those of copepods. This implies a rapid and efficient export of organic matter to depth. Even if these organisms represent $<$5\% of the overall planktonic biomass, the induced organic matter flux could be substantial. Here we present a first estimate of the influence of FFGM organisms on the export of particulate organic matter to the deep ocean based on the marine biogeochemical model NEMO-PISCES. In this new version of PISCES, two processes characterize FFGM: the preference for small organisms due to filter feeding, and the rapid sinking of carcasses and fecal pellets. To evaluate our modeled FFGM distribution, we compiled FFGM abundance observations into a monthly biomass climatology using a taxon-specific conversion. A model-observation comparison supports the model ability to quantify the global and large-scale patterns of FFGM biomass distribution, but reveals an urgent need to better understand the factors triggering the boom-and-bust FFGM dynamics before we can reproduce the observed spatio-temporal variability of FFGM. FFGM contribute strongly to carbon export at depth (0.4 Pg C yr$^{-1}$ at 1000 m), particularly in low-productivity region (up to 40\% of organic carbon export at 1000 m) where they dominate macrozooplankton by a factor of 2. The FFGM-induced export increases in importance with depth, with a simulated transfer efficiency close to one.