This paper aims to develop an adaptive inertial algorithm for solving bilevel variational inequalities with multivalued pseudomonotone operators in real Hilbert spaces and establish its strong convergence property. The algorithm does not need to know the prior information
of the Lipschitz constants and strong monotonicity coefficients of the associated mappings, incorporates inertial techniques and involves only one projection per iteration. The step sizes of the proposed algorithm are updated at each iteration by a cheap computation without any linesearch procedure. Some numerical experiments show that the proposed algorithm has competitive advantages over some existing algorithms.