Constant-pressure molecular dynamics simulations and an analysis of the local atomic structures have been performed to study the cooling rate dependence of some macroscopic and microscopic quantities in aluminium glass. Macroscopic quantities, enthalpy and density, see an observable but small dependence on the cooling rate. Icosahedral ordering units exhibit strong cooling rate dependence, which is responsible for the dependence of the enthalpy and the density on the cooling rate; while the almost independence of some microstructural units such as the 1541, 1431 and 1421 pairs of the cooling rate may lead to a small dependence of the enthalpy and the density on the cooling rate.