The quantum corrections to the entropy of the Barriola-Vilenkin black hole due to the massless gravitational field are calculated by using the brick-wall model.It is shown that the quantum corrections consist of two parts:One is a quadratic divergent term at the event horizon and is proportional to the surface area of the event horizon.The other is two logarithmically divergent terms which not only depend on the characteristics of the black hole but also on the spin of the field.The whole expression does not take the form of the scalar field.