ABSTRACT We study the cosmological build-up of pseudo-bulges using the L-Galaxies semi-analytical model for galaxy formation with a new approach for following separately the assembly of classical bulges and pseudo-bulges. Classical bulges are assumed to be the result of violent processes (i.e. mergers and starbursts), while the formation of pseudo-bulges is connected to the secular growth of discs. We apply the model to both the Millennium and the Millennium II simulations, in order to study our results across a wide range of stellar masses ($\rm 10^{7}\!-\!10^{11.5}\, {\rm M}_{⊙ }$). We find that z = 0 pseudo-bulges mainly reside in galaxies of $\mathit{ M}_{\rm stellar} \, {∼ }\, 10^{10}\!-\!10^{10.5}\, {\rm M}_{⊙ }$ ($\mathit{ M}_{\rm halo} \, {∼ }\, 10^{11.5}\!-\!10^{12}\, {\rm M}_{⊙ }$) and we recover structural properties of these objects (e.g. sizes and bulge-to-total ratios) that are in good agreement with observational results. Tracing their formation history, we find that pseudo-bulges assembled in galaxies with a very quiet merger history, as opposed to the host galaxies of classical bulges. Regarding the bulge structure, we find that $\, {∼ }\, 30{{\ \rm per\ cent}}$ of the galaxies with a predominant pseudo-bulge feature a composite structure, hosting both a pseudo- and a classical bulge component. The classical component typically constitutes ${∼ }\, 10{{\ \rm per\ cent}}$ of the total bulge galaxy mass. When looking at the properties of the host galaxies, we find that z = 0 pseudo-bulges are hosted by main-sequence galaxies, characterized by a stellar population which is generally younger compared to the one of the hosts of classical bulges.