With the test particle simulation method, we have investigated the stochastic motion of electron with the energy of 300 keV in a monochromatic magnetosonic (MS) wave field, which is motived by the violation of the assumption of quasi-linear theory when the strong MS waves (the amplitude up to ~ 1 nT) are presented in the Earth’s magnetosphere. First of all, the electron motion can become stochastic when the wave amplitude exceeds a certain threshold. If electron initially resonates with MS wave in the way of bounce resonance, as the bounce resonance order increases, the amplitude threshold of electron stochastic motion firstly increases until it reaches the peak at about the 11 order in our study, then the amplitude threshold begins a slow decline. More interestingly, we find that the coexistence of bounce and Landau resonances between electron and MS wave will significantly reduce the amplitude threshold. In some cases, the electron motion can become stochastic in the field of MS wave with amplitudes below 1 nT. Besides, if neither the bounce nor Landau resonance condition is satisfied at the initial, then the amplitude threshold of stochastic motion also shows the increasing trend for lower frequencies and the decreasing trend for higher frequencies, but the amplitude threshold is always very large (> 5 nT). Our study suggests that the electron stochastic motion should also be considered when modeling electron dynamics regulated by intense MS waves in the Earth’s magnetosphere.