Abstract: Laboratory testing showed that rheological property of polymer solution used in Daqing Oilfield agree with power-law mode. According to non-Newtonian fluid mechanics theory and mathematical method, and the plunger moving property taken into account, fluid velocity distribution, flow rate and pressure gradient equations were set up in the conditions concentric and eccentric of rod and tube annular space, and approximate solution were obtained. Calculating example showed that fluid velocity in rod and tube annular space changes steadily along with rod moving of up and down. In the condition of concentric of rod and tube, the stronger non-Newtonian property is,when θ=0,the smaller n is, the larger dimensionless maximum velocity is; when θ=π, the two dimensionless maximum velocities differ slightly in the condition of charging n.