This paper addresses the application of a data-based mechanistic (DBM) modelling approach using transfer function models (TFMs) with non-linear rainfall filtering to predict runoff generation from a semi-arid catchment (795 km2) in Tanzania. With DBM modelling, time series of rainfall and streamflow were allowed to suggest an appropriate model structure compatible with the data available. The model structures were evaluated by looking at how well the model fitted the data, and how well the parameters of the model were estimated. The results indicated that a parallel model structure is appropriate with a proportion of the runoff being routed through a fast flow pathway and the remainder through a slow flow pathway. Finally, the study employed a Generalized Likelihood Uncertainty Estimation (GLUE) methodology to evaluate the parameter sensitivity and predictive uncertainty based on the feasible parameter ranges chosen from the initial analysis of recession curves and calibration of the TFM. Results showed that parameters that control the slow flow pathway are relatively more sensitive than those that control the fast flow pathway of the hydrograph. Within the GLUE framework, it was found that multiple acceptable parameter sets give a range of predictions. This was found to be an advantage, since it allows the possibility of assessing the uncertainty in predictions as conditioned on the calibration data and then using that uncertainty as part of the decision-making process arising from any rainfall-runoff modelling project.