The objective of this project is to study the effect of nonzero curvature index on dark energy (DE) models. A variety of dark energy models are available in literature which can explain the observed accelerated expansion of the universe very well and are consistent with the observational data. But most of the dark energy models consider the spatial curvature to be zero and carry on the analysis for a spatially flat universe. However, recently there is a reheated debate on whether the spatial curvature of the universe is zero or not. In particular, there are arguments that if one considers the combined analysis of cosmic microwave background (CMB) anisotropy power spectra of the Planck Collaboration with the luminosity distance data, then a non-flat universe is favored at 99% confidence level. Additionally, recently it has been shown that the enhanced lensing amplitude in the CMB power spectrum also seems to suggest that the curvature index k may be positive. Hence a detailed investigation in this context is needed, focusing on the cosmological behavior of different cosmological parameters namely the dark energy density parameter, the equation-of-state parameter etc. in a non-flat universe.