We investigate cosmological dynamics and screening mechanism of the Dirac-Born-Infeld (DBI) Galileon model. The model has been divided into two regimes, one has positive signs in front of scalar field kinetic terms so-called the DBI Galileon, another one has negative signs and it is dubbed as the DBIonic Galileon. We find de Sitter solution and evolution of the Universe starting from radiation dominated era to late-time accelerated expansion in the DBI Galileon model without the presence of potential term. In one of the attractors, the ghost and Laplacian instabilities vanishes for the whole evolution. We find mixing of screening mechanisms between the Vainshtein mechanism and the DBIonic screening mechanism in the DBIonic Galileon model, in which a scale changing between these two mechanisms depends on a mass of a source.
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