Solar activities have a great impact on modern high-tech systems, such as human aerospace activities, 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 are highly anticipated. Based on the wavelet transform and empirical function fitting of the longest recorded data of the annual average relative sunspot number (ASN) series of 323 yr to date, this work decisively verifies the existence of the solar century cycles and confirms that its length is about 104.0 yr, and the magnitude has a slightly increasing trend on the timescale of several hundred years. Based on this long-term evolutionary trend, we predict solar cycles 25 and 26 by using phase similar prediction methods. As for solar cycle 25, its maximum ASN will be about 146.7 ± 33.40, obviously stronger than solar cycle 24. The peak year will occur approximately in 2024, and the period will be about 11 ± 1 yr. As for solar cycle 26, it will start around 2030, and reach its maximum between 2035 and 2036, with maximum ASN of about 133.0 ± 3.200, and period of about 10 yr.

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