Malaria is one of the most severe disease in the world. The projected climate change will probably alter the region and transmission potential of malaria in Africa. In this study, a climate-based mathematical model to investigate the impact of temperature and rainfall on malaria transmission is developed and analysed. The basic reproduction number (To) is derived along with stability analysis. The effect of the larval death rate on the reproduction number is also investigated. The model is validated on observed malaria transmission in Limpopo Province, South Africa, giving a reasonable fit and in particular, detecting accurately all the spikes in malaria prevalence. The model provides a numerical basis for further refinement towards prediction of the impact of climate variability on malaria transmission.