Context. As a key to chemical evolutionary studies, the distribution of elements in galactic provides a wealth of information to understand the individual star formation histories of galaxies. The r-process is a complex nucleosynthesis process, and the origin of r-process elements is heavily debated. Europium (Eu) is viewed as an almost pure r-process element. Accurate measurements of europium abundances in cool stars are essential for an enhanced understanding of the r-process mechanisms. Aims. We measure the abundance of Eu in solar spectra and a sample of metal-poor stars in the Galactic halo and metal-poor disk, with the metallicities ranging from -2.4 to -0.5 dex, using non-local thermodynamic equilibrium (NLTE) line formation. We compare these measurements with Galactic Chemical Evolution (GCE) models to explore the impact of the NLTE corrections on the contribution of r-process site in Galactic chemical evolution. Methods. In this work, we used NLTE line formation, as well as one-dimensional (1D) hydrostatic and spatial averages of three-dimensional hydrodynamical (<3D>) model atmospheres to measure the abundance of Eu based on both the Eu II 4129 & Aring; and Eu II 6645 & Aring; lines for solar spectra and metal-poor stars. Results. We find that for Eu II 4129 & Aring; line the NLTE modeling leads to higher (0.04 dex) solar Eu abundance in 1D and higher (0.07 dex) in <3D> NLTE while NLTE modeling leads to higher (0.01 dex) solar Eu abundance in 1D and lower (0.03 dex) in <3D> NLTE for Eu II 6645 & Aring; line. Although the NLTE corrections for the Eu II lambda 4129 & Aring; and Eu II lambda 6645 & Aring; lines are opposite, the discrepancy between the abundances derived from these individual lines reduces after applying NLTE corrections, highlighting the critical role of NLTE abundance determinations. By comparing these measurements with Galactic chemical evolution (GCE) models, we find that the amount of NLTE correction does not require significant change of the parameters for Eu production in GCE models.