The uncertainty and disturbance estimator (UDE)-based control is a robust control method, which is proposed as a replacement of the time-delay controller (TDC). With the filter design in the UDE-based controller, the challenging problem of designing a robust controller is converted into designing a filter. In this paper, a bounded UDE-based control is developed to deal with systems subject to uncertainties, disturbances and input constraints. The bounded controller output is achieved through nonlinear Lyapunov analysis, and an additional time-varying variable is introduced into the error dynamics to naturally avoid the integrator windup. The boundedness design is embedded into the existing UDE framework to form a bounded UDE-based controller without integrator windup via a simple structure and clear guidelines of parameter selections. Both theoretical analysis and simulation studies are provided to validate the proposed design.