A new two- stage noncollinear phase- matching optical parametric amplification (OPA) scheme,which can make full use of the phase- matching capability and the spectral gain range of specific nonlinear crystal to amplify neighboring spectral components of the seed by using individual phase- matching geometry in two- stage OPAs,is proposed to achieve a gain bandwidth close to one octave bandwidth.Numerical simulations are performed,in the case of a 4.5 mm- thick β - BaB2O4 (BBO) crystal and a laser pump source with wavelength of 532 nm and intensity of 5 GW/cm2.The results show that this scheme allows for an amplification of 480 nm spectral width spanning from 710 nm to 1190 nm corresponding to 0.75 octave bandwidth with a Fourier limited pulse duration of 5 fs,which equals to 1.6 times of the period of light oscillation.The phase distortions from parametric gain process and its impact on the temporal profile of the recompressed signal pulse are calculated.Results presented are capable of providing a theoretical basis for the design of optical parametric amplification system allowing for the generation of single-cycle pule.