The mass-conservative algorithm on the Yin-Yang grid is important for the construction and application of Yin-Yang grid in global atmospheric modeling studies. It is also an important index of model performance that ensures long-term stable integration and accurate computational results. In this study, the authors propose a mass-conservative algorithm of cell-wise bi-linear mass distribution and piece-wise linear flux distribution over the boundary. Compared to the conservative constraint that defines cell-wise constant mass distribution, the new algorithm improves the accuracy of advection computation on the Yin-Yang grid and enhances the stability of model integration. The flux-form advection equation is solved by using the CIP-CSLR (Constrained Interpolation Profiles-Conservative Semi-Lagrangian with Rational function) scheme. Several idealized tests, including a solid cosine-bell advection with non-divergent flow, a global transport of a sine-wave test and a test with smooth deformational flow, are conducted to compare the impact of cell-wise bi-linear distribution with that of the cell-wise constant distribution. The normalized errors and spatial distributions of scalars all suggest that the new scheme is capable of refining the global conservation status in model application, which would effectively improve the computational results of the conservative constraint on the Yin-Yang grid without greatly increasing the computational cost.