Under the high power injection condition of the wide-gap klystron amplifier (WKA), a second peak current appears besides the conventional optimally bunching current (or the first peak current) in the distribution of the fundamental integral current. Considering the electron bunching theory and the Particle-in-cell (PIC) simulation results together, the formation mechanism of the second peak current is discussed. The results indicate that the second peak current has a close relation with the electron multiple-overtaking phenomenon in the case of high voltage modulation coefficient. When the diode voltage is 600 kV, beam current is 5 kA and working frequency is 3.6 GHz, the beam modulation depth of the WKA is enhanced to 92% from 80% according to the multiple-overtaking mechanism. Simultaneously, the bunching current power is improved from 2.2 GW to 2.8 GW, and a 27 percent increment is obtained.