This paper presents pulse shortening of electron beams drifting through the input cavity and the idler cavity on an L-band long pulse relativistic klystron amplifier. We investigate one of the main mechanism of beam-current-pulse-shortening in which the interaction of asymmetric modes of cavity and the beams leads to the beams' expansion. Selective damping to suppress the asymmetric modes is described. The problem of beam-current-pulse-shortening through the idler cavity gap is removed to a certain extent after parameter adjustment of the input microwave and the idler cavity. In the experiment, the 446 kV,3.0 kA，1.3 μs hollow electron beams generated about 2.0 kA modulated current after two idler-cavity gaps, the width of electron beams' pulse is increased from 0.3 μs to 1.0 μs.