Wei,
Does the pump motor turn on/off or does the water flowing in the pump turn on/off, what we call surging??
If the pump is surging, the most likely cause is that the water is way too low.. It should be in the middle of your skimmer mouth. If not that, then the next most likely problem is that your Weir door is stuck up.. The weir door is between the water that the skimmer basket and it is supposed to float up and down with the water.
Thanks,
Jim R.