This paper proposes a general one-parameter discrete-time recurrent neural network (DT-RNN) model for solving the discrete-form time-varying augmented Sylvester matrix equation (DFTV-ASME). First, the DFTV-ASME is converted into its continuous-time form and further reformulated as a linear matrix equation problem. Then, a continuous-time recurrent neural network (CT-RNN) model is constructed following the design method of the zeroing neural network (ZNN). Subsequently, by discretizing the CT-RNN model using the general one-parameter square-pattern discretization (SPD) formula, the general one-parameter DT-RNN model is derived. Finally, the proposed model is evaluated through numerical experiments to demonstrate its effectiveness and examine how various parameters influence its performance.