An Ordinary Differential Equation(ODE) co-infection model of Tuberculosis-Lymphatic filariasis is proposed with 17 mutually disjoint compartments. We showed that the model is Mathematically and Epidemiologically well-posed and the disease-free equilibrium(DFE) of the co-infection model is locally asymptotically stable if R_O<1, it is unstable if R_O>1. The numerical results show that lymphatic \textit{filariasis} infection increases susceptibility to tuberculosis infection. This is in agreement with literature that, persons with lowered immunity such as HIV, diabetes, immune disorder etc are at a higher risk of contacting infectious diseases. We also found that increasing the rate of diagnosis and treatment of active tuberculosis and symptomatic lymphatic \textit{filariasis} cases, the incidence of co-infection in the community can be reduced, and that if resources are limited, efforts should be targeted at treating only the co-infected cases. Sensitivity analysis showed that increasing mosquito mortality rate, reducing the probability of mosquito infecting humans, reducing the probability of humans infecting mosquitoes, reducing mosquitoes recruitment rate by destroying mosquitoes breeding sites and reducing the number of times a mosquito bites human will bring down the reproduction number to less than unity.