By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a generalization of the main theorem proposed by X. P. Ding [Appl. Math. Comput. 113, No. 1, 67–80 (2000; Zbl 1020.49015)].