Thick-section plates made from a recently developed Al-Cu-Mg-Li alloy have been evaluated to understand the influence of microstructure on the anisotropy of tensile strengths after natural and artificial ageing treatment. Pancake-shaped grains with a coarse substructure and strong crystallographic texture with a beta-fibre orientation at the mid-thickness position are observed. In addition, an inhomogeneous distribution of T1 precipitates through the plate thickness has been revealed with the volume fraction of intragranular precipitates ~ 40% higher at the plate centre than the thickness position. Altogether these microstructural features contribute to the in-plane anisotropy of tensile strengths that is ~ 5% higher at the mid-thickness position than the 1/4 thickness position. The variation of ageing-induced T1 precipitates through the plate thickness further contributes to the through-thickness anisotropy that is ~ 3% higher in T8 temper as compared to T3 temper.