The hydrogen bonding of 1:1 complexes formed between formamide and water molecule have been completely investigated in the present study using density functional theory and second-order Moller-Plesset Perturbation (MP2) method, the large basis sets 6-311++g(d,p) and 6-311++g(2d,2p) have been employed to determine the equilibrium structure and vibrational frequencies of the interacting complexes. Four reasonable geometries on the potential energy hypersurface of formamide and water system are considered, three stable structures and one transition state are found with the global minimum being a cyclic double-hydrogen bonded structure. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The infrared spectrum frequencies, IR intensities and the vibrational frequency shifts are reported. Study of the blue shift of the n-π * transition of formamide with water shows that the hydrogen bond has a great contribution to the shift. Finally the solution phase studies are also carried out using the Onsager reaction field model with a range of dielectric constants from 2 to 80 at B3LYP/6-311++g(d,p) level.