  Solar activities have a great impact on modern high-tech systems, such as
human aerospace, satellite communication and navigation, deep space
exploration, and related scientific research. Therefore, studying the long -
term evolution trend of solar activity and accurately predicting the future
solar cycles is highly anticipated. Based on wavelet transform and empirical
function fitting of the longest recorded data of the annual average relative
sunspot number (ASN) series of 323 years to date, this work decisively verified
the existence of the solar century cycles and confirmed that its length is
about 104.0 years, and the magnitude has a slightly increasing trend on the
time scale of several hundreds of years. Based on this long-term evolutionary
trend, we predicted solar cycle 25 and 26 by using phase similar prediction
methods. As for the solar cycle 25, its maximum ASN will be about $146.7\pm
33.40$, obviously stronger than solar cycle 24. The peak year will occur
approximately in 2024, and the period is about $11\pm 1$ years. As for the
solar cycle 26, it will start around 2030, reach the maximum between 2035 and
2036, with maximum ASN of about $133.0\pm 3.200$, and the period is about 10
years.
