We investigate the possible effect of cosmological-constant type dark energy during the inflation period of the early universe. This is accommodated by a new dispersion relation in de Sitter space. The modified inflation model of a minimally coupled scalar field is still able to yield an observation-compatible scale-invariant primordial spectrum, simultaneously having the potential to generate a spectrum with lower power at large scales. A qualitative match to the WMAP 7-year data is presented. We obtain an Omega(Lambda) of the same order of that in the Lambda-CDM model. Possible relations between the de Sitter scenario and Doubly Special Relativity (DSR) are also discussed.