A new cosmological model based on the de Sitter gravity is investigated by dynamical analysis and numerical discussions.Via some transformations, the evolution equations of this model can form an autonomous system with 8 physical critical points.Among these critical points there exist one positive attractor and one negative attractor.The positive attractor describes the asymptotic behavior of late-time universe, which indicates that the universe will enter the exponential expansion phase, finally.Some numerical calculations are also carried out,which convince us of this conclusion derived from the dynamical analysis.