In this work we provide a contribution to Stark shift for some lines of neutral helium in plasmas. The mentioned shift is caused by the collisions of the unbounded electrons with helium atoms in plasmas. We calculate this contribution by taking into account only weak collisions. This contribution takes into consideration the presence of the local electric microfield created by the ions that constitute in part the plasma. The effect of this microfield modifies the electron trajectory and therefore changes the shift formula developed early by using the straight trajectories in the case of neutral emitters. Our new contribution to the Stark shift caused by electron's collision is applied to some HeI lines: 3188 , 3888 , 6678 and 7065 . Our results are confronted with the experimental and theoretical data from the literature which clearly show that the influence of the local electric microfield created by the ions on the Stark shift caused by electron's collision is not negligible and must be taken into account. It turns out that the correction to the theoretical shift for the lines under consideration tends to red.