The discovery of the Higgs mechanism within the context of spontaneous symmetry break- ing has offered a new perspective on early-time cosmic inflation and also on the relationship between elementary particles and dark energy, believed to drive the universe’s accelerating expansion. We suggest an inflation scenario dri v en by the Higgs boson within the frame- work of unimodular gravity, where the Higgs field acts as the inflaton and has a significant non-minimal coupling to the gravity. We present a detailed analysis of the problem in the Jordan and then Einstein frame for a unimodular Higgs inflation, followed by a comparison of our findings with the cosmic microwave background observations made by the Planck Collaboration and other joint data sets. Ther efor e, new constraints ar e imposed on the non- minimal coupling parameter, ξ, by determining the magnitudes r equir ed for effecti v e cosmic infla tion. We demonstra te tha t a substantial non-minimal coupling of order ξ∼10 2 –10 4 is r equir ed for this model to match with the observed primordial spectrum.