In this work, we present the structural and the spectroscopic properties of the alkaline earth BeLi²⁺ ion for all the electronic states dissociating into Be⁺(2s, 2p, 3s, 3p, 3d, 4s, 4p, and 4d) + Li⁺ and Be²⁺ + Li (2s and 2p). We have used an ab initio approach involving a non-empirical pseudopoential for the Li⁺ and Be²⁺ cores and core-core and core-valence correlation corrections. For our best knoweledge, the adiabatic potential energy curves and the spectroscopic constants for nearly 18 electronic states of ²Σ⁺, ²Π and ²Δ symmetries are determined here for the first time. As neither experimental nor theoretical data are available for BeLi²⁺, our results are discussed and compared with similar systems such as BeH²⁺. Numerous avoided crossings between the electronic states of ²[loc=pre]Σ⁺ and ²Π symmetries have been localised and analysed. Their existences are related to the interaction between the potential energy curves and the charge transfer process between the two ionic systems Be⁽²⁺⁾Li and Be⁺Li⁺. Furthermore, we have calculated the adiabatic transition dipole moments from X²Σ⁺, 2²Σ⁺ and 3²Σ⁺ states to the higher electronic states of the same symmetry. This study represents the necessary initial step towards the investigation of the charge transfer processes in collision between Be⁺-Li⁺ and Be²⁺-Li.