Most of reported policy-relevant topping elements in the Earth’s climate system are related to the variability of the Atlantic Meridional Overturning Circulation (AMOC), which can transport the excess heat absorbed by low latitudes to high latitudes and maintain the energy balance of the global climate system. Theoretical analysis shows that AMOC may have two different stable States. Under the background of global warming, the collapse of AMOC due to unstable changes will have a serious impact on the global climate. Some studies point out that the change of AMOC in the past hundred years has shown a trend of unstable development or even collapse, and give early warning signals based on observations. Here, we briefly review the perspective on the AMOC collapse derived from both model simulations and observational data analysis. We show that the early warning signal of AMOC instability given by previous studies mainly comes from the uncertainty of observation data, which is the performance of observation system bias. We point out that it is impossible to draw a conclusion about the instability of AMOC based on the observational data. This work highly emphasizes the importance of strengthening ocean observation for global climate change research.