Abstract: According to the characteristics of parachute,based on 0-thickness assumption of canopy,axisymmetric assumption of parachute,and steady assumption of flowfield,a fluid dynamics computational model was established.By solving RNG(Renormalization Group) k-epsilon turbulence N-S Equations over low angle of attack range of 0~5°,the numerical simulation result was in good agreement with the relative experiments.It was found that the direct connection of saddle point in the axisymmetric parachute sectional flowfield of 0° angle of attack was unstable.With the increase of angle of attack,the types and connection models of singular point will be changed.Limit cycles will appear in the vortex ring near the parachute surface.Also new saddle points and a nodal point will appear in the section flowfield.With the further rising of angle of attack,the area of limit cycles will decrease until limit cycles disappeared.The nodal point will change into a half-node and attach to the parachute surface.The results indicate that the topological structures of sectional flowfield of an axisymmetric parachute at low angle of attack accord with topological rules. The gained evolvement rules of the flowfield characteristics of an axisymmetric parachute in terminal descent here may lay foundation for further investigating parachute flow mechanism and fluid-structure coupling.