This paper investigates the transmission of malaria and attempts to control the disease using mathematical model. In this research, we analyse the dynamics of malaria using a system of nine differential equations. The analysis carried out reveals that if the basic reproduction number Ro<l, the disease free equilibrium point is stable, but if Ro>l, the disease free equilibrium is unstable. We conclude from the analysis that there is no endemic equilibrium and malaria – free society is feasible. Our analysis also reveals that certain control strategies are capable of reducing malaria transmission. These are: sufficient treatment of infected people with drugs; spraying of insecticides and the use of insecticide-treated bed nets; destruction of mosquito breeding sites and campaign strategy for malaria control