The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.