The parameter uncertainty in hydrological modelling has been accorded much attention in the recent past. Parameter uncertainty is a major source of overall model unreliability. In this study, the HydroPSO R package was used to assess parameter identification and uncertainty for the Soil and Water Assessment Tool (SWAT) model applied in the upper reaches of Nzoia River Basin. Fourteen parameters were selected based on previous studies and parameter sensitivity analysis using the Latin Hypercube Sampling method. Based on the optimum parameter set, the simulated flow corresponded well with the observed flow with daily Percent Bias (PBIAS), coefficient of determination (R2) and Nash–Sutcliffe efficiency (NSE) of -1.4, 0.73 and 0.72, respectively. For monthly calibration, these values were -1.4, 0.78 and 0.77, respectively. The results of this study show uncertainty in parameter identification. The posterior distributions of the parameter values were not normally distributed and the uncertainty ranges of the parameters varied widely. The low flows (Q5) were overestimated with a 13.8% bias while the Q50 and Q95 flows were underestimated with -4.2% and -13.1% biases respectively. Further analysis indicated that the contribution of parameter uncertainty to stream flow simulation was substantial with 35% of the observed flow data falling within the 95% simulation confidence interval for the calibration period. Different parameter sets gave the same correlation between the simulated and observed flows. A multiobjective analysis of the hydrological modeling uncertainties emanating from model selection, calibration procedure and calibration data errors in the basin is therefore recommended.