In this paper, a deterministic ordinary differential equations model for the transmission dynamics of maize streak virus disease (MSVD) in maize plants is proposed and analyzed qualitatively. Using the next generation matrix approach, the basic reproduction number, ${\mathcal{R}}_0$ with respect to the MSVD free equilibrium is found to be $4.7065\approx 5$. The conditions for local stability of the disease-free equilibrium and endemic equilibrium points were established. From the results, the disease-free equilibrium point was found to be unstable whenever ${\mathcal{R}}_0>1$ and the endemic equilibrium point was found to be locally asymptotically stable whenever ${\mathcal{R}}_0>1$. The sensitivity indices of various parameters with respect to the MSVD eradication or spreading were determined. It was found that $b,{\beta }_1,{\beta }_{11},$ and ${\beta }_2$ are the parameters that are directly related to ${\mathcal{R}}_0$, and $H_2,\mu ,{\mu }_1$ and $\gamma$ are inversely related to ${\mathcal{R}}_0$. Numerical simulation was performed and displayed graphically to justify the analytical results.