An optical parametric chirped pulse amplification (OPCPA) physical model is presented, and a splitstep Fourier technique is used to develop a three-dimensional OPA+CPA numerical code (3D OPA+CPA code), which can be used to model the broadband amplification, gaining narrowing, self-phase modulation, spatial selffocusing and the temporal signal-to-noise ratio (SNR) of OPCPA laser facility, and to optimize the design of OPCPA system. The SG-II-U-PW laser facility is studied numerically using this 3D OPCPA code, and the calculated results show that the ninth beam line is suitable to be modified for meeting the design goal of the SGII-U PW project. The 3D OPA + CPA code can be modified with ease to model and optimize the designs of femtosecond OPCPA system, and especially the future laser facility with exawatt (1018 W) peak intensity.