This article investigates the sampled-data disturbance rejection control problem for a class of non-integral-chain systems with mismatched uncertainties. Aiming to reject the adverse effects caused by general mismatched uncertainties via digital control strategy, a new generalized discrete-time extended state observer is first proposed to estimate the lumped disturbances in the sampling point. A disturbance rejection control law is then constructed in a sampled-data form, which will lead to easier implementation in practices. By carefully selecting the control gains and a sampling period sufficiently small to restrain the state growth under a zero-order-holder input, the bounded-input bounded-output stability of the hybrid closed-loop system and the disturbance rejection ability are delicately proved even the controller is dormant within two neighbor sampling points. Numerical simulation results demonstrate the feasibility and efficacy of the proposed method.