The authors have examined the effects of superposition of a low-frequency ac voltage and a high-frequency ac voltage on the growth of water trees in polyethylene, and have made it clear that the number of voltage zero-crossings is a decisive factor of water tree growth. In the present research, a short-duration high-frequency (2 kHz) voltage was superposed repeatedly onto a continuously applied low-frequency (0.5, 1.0, 3.0 or 5.0 Hz) voltage in synchronous with the low-frequency voltage either at its positive and negative maxima or at each zero-crossing point. By applying such superposed voltages to a low-density polyethylene sheet with a water needle electrode and a counter plane electrode, the length of a grown water tree was evaluated. As a result, it has become clear that the water tree length is longer when the high-frequency voltage is superposed at each zero-crossing point of the low-frequency voltage. This result supports the above-mentioned assumption that the number of voltage zero-crossings plays a significant role in the growth of water trees.