A computational study of the electronic structure of the SrKr and Sr+Kr molecular systems is presented in this paper. The computational scheme is based on the Full Configuration Interaction (FCI) method and semi-empirical pseudo-potential approach of the atomic core Sr2+ with Gaussian-type-orbital (GTO) basis sets. We have calculated the potential energy surfaces (PESs), spectroscopic parameters, electric dipole moments, and the vibrational levels' spacing for the electronic states of the SrKr molecule and its Sr+Kr ion. The accuracy of the current spectroscopic results is discussed by comparing them tothe available experimental and theoretical data. It is interesting to note that the relevant data of the Sr+Kr molecular ion show significant shapes in the higher 2Σ+ electric states, which allows us to check the intense transition in electric dipole moment and to carry out a diabatic investigation in the future.