Abstract: Computing volumetric domain parameterizations is a fundamental problem in isogeometric analysis. However, existing methods cannot reduce the distortion of the parameterization effectively. This paper proposes a novel algorithm to compute bijective volumetric domain parameterizations with low distortion. This algorithm introduces the geometry of the parameter domain into the distortion optimization as variables, which leads to lower distortion. Firstly, compute the mapping between the computational domain and the parameter domain in order to construct the boundary correspondences. Secondly, construct a low-distortion discrete volumetric domain parameterization mapping according to the boundary correspondences. Finally, approximate the discrete volumetric domain mapping with B-spline basis to obtain B-spline volumetric domain parameterizations. The capability and feasibility of the method are demonstrated over 215 complex 3D models, and the symmetric Dirichlet distortion energy of the proposed method is 30.91% and 29.74% lower on average than the two experimental comparison methods, respectively.