We investigate intermediate inflation in the framework of a Galileon scalar field. To this aim, we first obtain the inflationary observables, including the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index, as well as the non-Gaussianity parameters. Then, we examine the observational viability of the intermediate inflation within the framework of a Galileon scenario. Our results show that although the prediction of intermediate inflation in the standard framework is completely ruled out by the Planck 2015 observations, it can be put inside the allowed regions of the Planck 2015 TT,TE,EE+lowP data in the Galileon setting. Moreover, we determine the parameter space of the Galileon intermediate inflation for which the model is consistent with the Planck 2015 data. Besides, we derive the consistency relation in the Galileon scenario, and find that it differs from the standard inflation. We also estimate the running of the scalar spectral index and find that it is in well agreement with the 95% CL constraint of the Planck 2015 results. Finally, we evaluate the local, equilateral, orthogonal, and enfolded non-Gaussianity parameters, and conclude that not only is the shape of non-Gaussianity approximately close to the equilateral one, but that it also satisfies the 68% CL bound from the Planck 2015 data.The inflationary paradigm, which was first proposed in the early 1980s, is a theoretical framework to describe the early stages of the evolution of the universe. Inflation addresses and partially solves some problems of the standard Big Bang theory such as the flatness problem, the horizon problem, and the magnetic monopole problem [1][2][3][4][5][6][7][8]. Furthermore, inflation as an important part of modern cosmology provides the most convincing explanation for the origin of the anisotropy observed in the CMB radiation, as well as for the Large Scale Structure (LSS) formation in the universe [9][10][11][12]. According to the standard inflationary scenario, a canonical scalar field that is minimally coupled to the Einstein gravity, can explain how our universe expands at an accelerating rate during the inflationary era [13,14]. In the context of inflation, two different approaches have usually been used to study inflationary scenarios: one based on scale factor, and the other case on the potential of scalar field inspired by particle physics. So far, different versions of inflation models with specific potentials or scale factors in the framework of standard inflationary scenario have been studied in the light of observational data [15][16][17][18][19].An interesting class of inflationary models, named G-inflation or Galileon models of inflation, have been discussed by many authors in which inflation is derived by the Galileon field . The Galileon field is a scalar field whose action is invariant under the Galilean symmetry ∂ µ φ → ∂ µ φ + b µ in the Minkowski spacetime [42][43][44]. This scalar field theory was first proposed in [42], and was inspired by the Dvali-Gabadadze-Po...