An inexact proximal point algorithm using quasi-distances is introduced to give a solution of a minimization problem in the Euclidean space. This algorithm has been motivated by the proximal method introduced by Attouch, Bolte and Svaiter [1] but in this case we consider quasi-distance instead of the Euclidean distance, functions satisfying the Kurdyka-Lojasewicz inequality, vector errors in the critical point of the proximal subproblems. We obtain, under some additional assumptions, the global convergence of the sequence generated by the algorithm to a critical point of the problem.