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In this study, how well the climate models reproduce variability in observed rainfall was assessed based on General Circulation Models (GCMs) from phase 3 and phase 5 of the Coupled Model Inter-comparison Project, i.e., CMIP3 and CMIP5, respectively as well as the Regional Climate Models (RCMs) of COordinated Regional Climate Downscaling EXperiment (CORDEX) over Africa. Observed and climate model based daily rainfall across the Lake Victoria Basin, which is one of the wettest parts of Africa, was considered. Temporal variability was assessed based on the coefficient of variation of daily and annual rainfall, and the maximum dry and wet spell in each year. Furthermore, variation in daily rainfall was assessed in terms of the long-range dependence. Comparison of variability results from observed and climate model based rainfall was made. It was found that the capacity to reproduce variability in observed wet and dry conditions depends on the specific GCM (of CMIP3 or CMIP5) or CORDEX RCM. However, the CORDEX RCMs replicated variability in observed daily rainfall better than the CMIP3 and CMIP5 GCMs. This was due to the spatial resolutions of the CORDEX RCMs which are higher than those of the CMIP3 and CMIP5 GCMs. The ensemble mean of the coefficients of correlation between the variability in observed and that of climate model based rainfall was close to zero for both the GCMs or RCMs. This suggests that analyses can be done on a case by case basis. In other words, GCMs or RCMs which adequately reproduce variability in observed wet and dry conditions can be considered for further statistical analysis of the changes especially on the basis of statistical methods for downscaling. For daily timescale, both the GCMs and RCMs from all the three sets of climate models generally exhibited poor performance in capturing the time of occurrences and the magnitudes of rainfall events (when considered in a combined way). To reliably assess long-term rainfall changes, it is vital to characterize natural variation in terms of the statistical dependence. With respect to natural variability of rainfall at local scales, there is room for further improvement of the climate models; however, whether theory of fractals and/or concepts of scaling behavior or self-similarity can explicitly contribute in that respect is a crucial consideration. Results from this study gave some insights in the reasonableness of the future rainfall projections.