Abstract: In a solenoidel focusing field, the centroid of any slice in an electron beam will execute cyclotron oscillation, if the magnetic –axis is tilted from the axis of accelerator. The energy variation within the beam pulse will make cyclotron oscillation develope corkscrew oscillation. In this paper, the trajectory of beam centroid is analytically found, the expression of the effective radius for an electron beam is given, and the method to reduce corkscrew oscillation is simply discussed.