The paper investigates a finite-dimensional servomechanism design for a parabolic distributed parameter system with constant disturbances, by discrete-time input-output data. The problem is to design a discrete-time feedback controller such that the resulting continuous-time closed-loop system will be stable and the discrete-time controlled outputs will be regulated. With some assumptions with respect to a control operator and an output operator, the paper presents explicit sufficient conditions for the existence of a discrete-time feedback controller which stabilizes and regulates the system. A finite-dimensional design procedure of a servomechanism is given and it is shown that the discrete-time controlled outputs will converge to the constant reference vectors with an arbitrarily assignable decay rate. In the design procedure it is necessary to construct a finite-dimensional discrete-time state observer in order to estimate the system state at sampling times from observations