We report a high-power, kilohertz, ultrafast optical parametric amplifier (OPA) that is seeded by white-light continuum and contains three amplification stages. Two 3-mm KTA crystals cut in type-II phase-matching configuration are used in the OPA system which is capable of producing up to 70 μJ, 140 fs infrared laser pulses at wavelength ranging from 2.9 to 4 μm. A full-scaled numerical simulation on the OPA system was performed. Actual white-light seeded signal pulse and finite phase-matching bandwidth were taken into account in the calculation. Material dispersion and linear absorption of all the optical components involved were properly incorporated. The simulation results match the experimental results almost perfectly. Our simulation provides an essential tool to design and optimize the OPA systems. A step-by-step design procedure based on this simulation algorithm is presented.