Solar activities have obvious effects on earth's climate. Many scientists have studied the relationship between solar activities and climate change, and a lot of papers have been published in this field. The relative sunspot numbers is an important factor in the research of solar activities. Wavelet transform is a fine method to analyze time serials periods. By using different data, the periods are different. In the past time, many scholars had analyzed solar activities by others statistical methods, found that changes of solar activity have periods of 5-6 years, 11 years, 22 years, 80-100 years, and so on. The periods are so disunity that they can't be better used to forecast change trend of solar activities. In this paper, being applied to analysis of solar activities, the wavelet transform method was introduced to analyze periods change, and found some meaningful results. The relative sunspot numbers change with periods of 10.7 year and 101 year. The 10.7 year period is remarkable, and it's amplitude varies with time. In 1935 to 2000, the amplitude of 10.7 year period are especially distinct. The solar activities exist strong or weak phases. Abrupt change occurred in 1950 year, and solar activities became stronger since 1950. It is predicled that the solar activity will be weaker in the near future.