The phenomenon of solar magnetic activity (sunspot numbers, sunspot areas, flare index, filament and prominence, etc.) has obvious amplitude asymmetry and phases asynchronous in the northern and southern hemispheres. This phenomenon is called hemispheric coupling of the solar activity cycle. The hemispheric coupling phenomenon of solar activity cycle is a manifestation of the evolution of the solar magnetic field, discovered as early as the middle of the 20th century. The characteristics of hemisphere coupling distribution, the speed and mode changes of the meridional circulation velocity, the hemispheric phase delay of the reversal of the magnetic field polarity, and the precursory characteristics of gestation or induction of super-minimal periods are considered to be the core ways to understand the theory of generator and dynamic evolution process. It is also seen as an important channel to explore the mechanism of occasional enhancement of solar activity ( such as the modern maximum ) or occasional weakening of solar activity( such as the Maunder minimum ). Here, we investigate the amplitude asymmetry of the hemispheric sunspot activity， mainly based on the data of Sunspot Relative Numbers from March 1939 to September 2019 of Solar Science Observatory, NAOJ Mitaka, supplemented by sunspot number from November 2008 to October 2019 of Kanzelhöhe Solar Observatory, sunspot areas from May 1874 to September 2016 of Royal Greenwich Observatory (RGO) and international sunspot numbers (SILSO) from November 2008 to October 2019. Four meaningful results as following: 1) Sunspot Relative Numbers is highly correlated with the International Sunspot Number; 2) Confirmed that the southern hemisphere are dominant of the northern hemisphere from cycle 17 to cycle 19, and the northern hemisphere are dominant of the southern hemisphere from cycle 20 to cycle 24, there is about a longterm period of 8 cycles; 3) During Cycle 24, northern hemisphere is dominant of southern hemisphere except for the the time of polarity reversed (the southern hemisphere is ahead of the northern hemisphere); 4) There are three enhanced periodic signals on the LSP power spectrum：around 8.5 years (a small range around the 11year cycle band), 30 and 50 years, and 3-5years. Finally, we make a conclusion, and give the discussion about the future research concern the hemisphere coupling of the solar activity cycle.
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