A simple ocean circulation model is used to study the multicentennial variability of the Atlantic meridional overturning circulation (AMOC). Firstly, a latitude-averaged 2-D ocean circulation model is derived, and the control equation and key parameters for AMOC are established. Then, through numerical methods, a reasonable mean climate of AMOC is simulated under appropriate boundary conditions and external forcings. To excite the multicentennial variability of AMOC, a long-term integration is carried out by adding a random salinity flux forcing to the subpolar surface layer of the Northern Hemisphere. Power spectrum analysis results show that AMOC can exhibit oscillations with a period of about 260 years. The first spatial mode obtained from the EOF decomposition of AMOC exhibits signals primarily in the deeper ocean basins, indicating that the multicentennial variability may be closely linked to changes in the deeper ocean. The relationship between the oscillation period and the volume of the ocean basin as well as the strength of AMOC is also explored. Larger basin volumes are associated with longer oscillation periods, while stronger AMOC correlates with shorter periods.