Bilingualism is a sustained experience associated with structural changes in cortical grey matter (GM) morphology. Apart from a few studies, a dominant method used to assess bilingualism-induced GM changes has been the voxel-based morphometry (VBM) analysis. While VBM is sensitive to GM volume/density differences in general, it cannot be used to identify whether the observed difference is due to relative changes in, e.g., cortical thickness, area or folding, as it uses a single combined measure of them all. Here, we used surface-based analysis (SBA) approach to investigate whether early acquisition of a second language (L2) affects the cortical GM morphology relative to late L2 acquisition. More specifically, our aim was to test a hypothesis that early acquisition of two languages induces GM changes that are predominantly surface area-driven, while late acquisition is supposedly characterised with primarily thickness-driven changes. To this end, several surface-based measures were concurrently compared between the groups. In line with the hypothesis, the results revealed that early bilingual experience is associated with significantly extended cortical surface area over the left pars opercularis and the right superior temporal gyrus. Contrary to our expectations, however, we found no evidence supporting the postulated association between late L2 acquisition and increased cortical thickness. Nevertheless, our study highlights the importance of including cortical surface measures when investigating bilingualism-related GM modulations.