At the present time the direct field oriented (DFO) control is the widespread used control technique in high performance induction motor (IM) drive. As it is well known, the IM drive performances are strictly connected to the rotor flux observation. The motor parameter variations cause the observer de-tuning and, hence, the IM drive performance degradation. In the present paper an adaptive observer is proposed which allows the on-line rotor time constant tuning. The identification of the rotor time constant is performed by a MRAS approach. The adaptive observer is synthesised using the Lyapunov stability theory. To improve the speed convergence of the identifier and the selectivity characteristic of the proposed adaptive observer, a time varying gain has been introduced. Simulations conducted on a DFO controlled drive, are reported to evidence the good performance of the proposed observer.