In tokamak plasma, the discharge will turn into runaway discharge from normal discharge if the plasma density becomes very low. The discharge will enter into slide-away discharge if the density decays to a critical one, in which the confinement of plasma (exactly supper thermal electrons) is better than that in normal discharge. The confinement of plasma and the anomalous Doppler instability during slide-away discharge gas puffing are investigated. The effect of gas puffing on runaway electrons during slide-away discharge is also studied in this paper. It is found that the anomalous Doppler instability can be suppressed by the gas puffing during slide-away discharge, while the confinement of plasma becomes poor, and many high energy runaway electrons occur during gas puffing.