The formation and propagation mechanisms of atmospheric-pressure cold plasma jets and the influence of air molecules including the nitrogen and the oxygen molecules on them are investigated by a one-dimensional fluid model in a needle-to-plane discharge in helium. It is shown that the air molecules have significant influence on the bullet velocity and the plasma jet length. As the air impurity level increases, the peak velocity of plasma bullet starts to increase and then drops sharply, and the plasma jet length is decreased exponentially. It is also found that the increase of the applied voltage results in the increase of bullet propagation velocity, which is in good agreement with experimental results. (C) 2011 Elsevier B. V. All rights reserved.