Abrupt jumps in the density of helicon discharge have been observed following continuous variation of parameters such as the external magnetic field and the radio frequency (RF) input power. In this study, we show the spatio-temporal behavior of such density jumps and the mode transition in a helicon plasma. It is found that the density jump process is characterized by two temporal phases with the contribution of higher axial modes, changing the antenna current (and thus the RF power). We also investigated the effect of the neutral depletion on the local plasma equilibrium. The temporal fluctuation of the plasma density caused by the neutral depletion was observed.