Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact. In some practical problems, we can only obtain approximate values of the objective function and its gradient. It is necessary to design optimization algorithms that can utilize inexact first-order information. In this paper, we propose an adaptive regularized quasi-Newton method to solve such problems. Under some mild conditions, we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method. Detailed implementations of our method, including the subspace technique to reduce the amount of computation, are presented. Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method, which can utilize the inexact first-order information effectively.