Optical parametric chirped pulse amplification (OPCPA) shows great potential in producing ultrashort high-intensity pulses because of its large gain bandwidth. Quasi-parametric chirped pulse amplification (QPCPA) may further extend the bandwidth, but the behavior of QPCPA at a limited pump intensity (e.g., ≤5 GW/cm2 in a nanosecond pumped QPCPA) is not fully investigated yet. We have discussed in detail the ultra-broadband amplification and the noncollinear phase-matching geometry in QPCPA. We have modeled and developed a novel noncollinear geometry in QPCPA namely ’triple-wavelength phase-matching geometry’ which provides two additional phase-matching points around the phase-matching point at the center wavelength. Our analysis demonstrates that the triple-wavelength phase-matching geometry can support stable, ultra-broadband amplification in QPCPA. The numerical simulation results show that ultrashort pulse with a pulse duration of 7.92 fs can be achieved in QPCPA when the pump intensity is limited to 5 GW/cm2, calculated using the nonlinear coefficient of YCOB.