In this paper, a deterministic mathematical model for the transmission dynamics of Visceral leishmaniasis (VL) was formulated and analyzed. The basic reproductive number R0 was obtained using the next generation matrix method. The model which was parameterized using the 2011 cases of Visceral Leishmaniasis in South Sudan, was used to assess two control measures. Numerical simulation reveals that the exposed population is reduced by high detection rate, and low biting rate of sandflies. Further, our model simulation gave the values of the contact rate of susceptible human, α1 and the detection rate of new cases, σ at which the basic reproductive number is less than one, (R0 < 1), equal to one (R0 = 1) and greater than one (R0 > 1).