Aiming at the high-quality parameterization problem of constructing a complex Three-Dimensional （3D） computational domain with given boundary conditions in isogeometric analysis， a 3D domain parameterization method based on high-dimensional quasi-conformal mapping was proposed. The core of the proposed method is to establish a nonlinear optimization model that describe the bijectivity， angular distortion， and volume distortion of the mapping simultaneously. Firstly， the high-dimensional quasi-conformal mapping theory was used to derive a new formula for measuring angular distortion in 3D space. Then， exponential variable and volume constant were introduced into the optimization model， and geometrical meaning of the Jacobi matrix was exploited to achieve the goal of adding volume distortion while preserving mapping bijectivity. Finally， Alternating Direction Method of Multipliers （ADMM） framework was combined with L-BFGS （Limited-memory Broyden-Fletcher-Goldfarb-Shanno） method to decompose the original problem into tractable subproblems and they were solved alternatively. Experimental results show that the proposed method guarantees global bijectivity on the experimental model； the proposed method has the orthogonality increased by about 5.8% compared to ADMM-LRP （ADMM algorithm for Low-Rank Parameterization）， and has the volume uniformity improved by about 34.4% compared to TTS （Tet-To-Spline optimization strategy）. It can be seen that the proposed method achieves high-quality parameterization， ensures bijectivity of mapping， and reduces angular distortion as well as and volume distortion.