To explore whether the dispersion of sediments in the North Atlantic can be related to modern and past Atlantic Meridional Overturning Circulation (AMOC) flow speed, particle size distributions (weight%, Sortable Silt mean grain size) and grain-size separated (0–4, 4–10, 10–20, 20–30, 30–40 and 40–63 μm) Sm-Nd isotopes and trace element concentrations are measured on 12 cores along the flow-path of Western Boundary Undercurrent and in the central North Atlantic since the Last glacial Maximum (LGM). North Atlantic is a useful place to explore how size-specific sediment provenance is related to sedimentary inputs and deep-current advection because mantle-derived materials in Iceland is a unique sedimentary source compared to crustal-derived terranes in Europe, Greenland and North America. The four main processes transporting sediments from continents to the North Atlantic (bottom currents, turbidity currents, ice-rafting events, airborne inputs) can be well distinguished through the size-specific physical and geochemical records. When primarily advected by the bottom currents, Holocene sediments show that the finer-sized fractions (0–4, 4–10, 10–20 μm) were transported further, and the coarser size fraction (40–63 μm) matched local inputs. In the deep coretops (> 2700 m) proximal to southern Greenland, fine-slit size fraction (10–20 μm) instead of clay size fraction (0–4 μm) observed more Icelandic-material contribution. In the past, the 20–30, 30–40 and 40–63 μm particles in the shallower Iceland-proximal core (1249 m) reflect Icelandic composition variation due to the abrupt volcanic eruption around 13–9 ka; while in the deeper Iceland-proximal core (2303 m) they were sensitive to the changing bottom flow speed. Downstream in cores proximal to southern Greenland (> 2272 m) and eastern North America (3555 m), composition of the 20–63 μm sediments could be used as an indicator for the retreating of the Greenland and Laurentide Ice Sheets which affect the sediment accessibility of the covered geological terranes; while the 0–4, 4–10 and 10–20 μm particles were more sensitive towards the changing direction (northern-sourced or southern-sourced) and velocity of the bottom current. In the open North Atlantic, the composition of the 0–10 μm particles were less variable between the cold and warm climate intervals compared to the 10–63 μm particles, and the 30–40 and 40–63 μm size fractions were sensitive towards both ice-rafting events and bottom flow direction. During LGM, shallower and vigorous northern-sourced water (NSW) was observed overlaying the deeper southern-sourced water (SSW), with the boundary between 2133 to 2303 m in southern Iceland, and ~ 2272 m in southern Greenland. Reduced NSW occurred during Heinrich Stadial 1, until AMOC above ~ 3500 m recovered to vigorous modern-like version no later than ~ 13.5 ka. Sluggish overflow was observed in North Atlantic between 12.2–11.7 ka above ~ 3500 m. Reduction of Iceland-Scotland Overflow Water occurred around 9.7 ka, and started recovering to its modern vigorous no later than ~ 8.6 ka. These relative past AMOC strength variations (vigorous/sluggish) are firstly converted to actual bottom-current speed (in cm/s) using laminar advection model in this work: vertical settling velocity of particle having the most Icelandic contribution is calculated by Stokes’ Law, and the lateral deep-sea current speed is calculated when the vertical settling depth and the lateral advection distance of the particle traveled before settling are constrained. Primary modelling errors originating from temperature/salinity variations in past deep seawater, winnowing process in fine particles, basaltic-signature dilution by crustal input, and lateral advection pathways of Icelandic-material are further discussed, indicating relatively low modelling error (< ~ 10–20 %). The modelling results agree well with modern deep-sea current speed measurements and backtrack-trajectory eddy resolving model (Ocean model for the Earth Simulator, OFES18), indicating reasonable quantifications of past AMOC flow speeds.