We analyze the structure and rheological properties of ring and linear polymers under shear byusing the non-equilibrium molecular dynamics simulation. The simulation results show that compared with the ring chains, the linear polymers do not present prominent stress over shoot phenomenon. Since the overshoot reflects the maximum flow-induced deformation of the polymer, this qualitative observation already implies that the ring experience less deformation than its linear precursor in simple shear flow. This is consistent with the recent experimental result. In order to further study the molecular mechanism of this phenomenon, the segmental structure and orientation angle distribution as a function of strain under the different Weissenberg numbers are given in this study. The weak overshoot of the stretching of the ring polymers proves that the weak shear thinning and peak strain are due to the weak deformation of the segment chain of the ring in the shear flow. The rheological properties of linear and ring system are extracted from the stress-strain curves, can be used further to analyze the data. The peak strain γ_max as afunction of Wi_R follows a power-law with an exponent of 0.3 for linear polymer at Wi_R>1, however, for the ring system thepeak strain follows a power-law with an exponent of 0.1. The parameter η_max/η_steady is also the measure of the effective chain deformation at a steady state. The data show its progressive increase with Wi_R increasing, and follows a power-law with a scaling slop of 0.13 and 0.08 for linear and ring polymers, respectively. The peak stress σ_max as a function of Wi_R is also extracted from stress-strain curve. The two investigated systems both obey the scaling law with an exponent of 0.5. The normalized steady-state shear viscosity obeys a shear thinning slop of –0.86 for the linear polymer, the ring polymer obeysa shear thinning slop of –0.4. According to the gyration tensor and orientation angle, the power-law relationship between stretching and orientation is also given in this work.