In this paper, a novel method - electron waves interference method - is presented to study Fowler-Nordheim tunneling current oscillations. Using this new analysis, the applied voltage V at the extrema of Fowler-Nordheim tunneling oscillations can be accurately and simply determined. A phase shift of pi/4 when electron traverses the forbidden band of perfect medium barrier once is observed by using interference method. Some phenomena observed in experiment can be easy to explain by this method. The extrema of oscillations can be used to determine the barrier thickness in metal-oxide-semiconductor device and the average effective electron mass in the conduction band of the barrier. An important feature of this method is that it is applicable to various shapes of potential barriers and wells.