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The goal of this research is to proof the wellposedness of scalar field equation on spatially compact spacetime Riemannian manifold. The first step of this work is to construct the equation of motion from lagrangian of scalar field with non-minimal coupling, where the coupling interaction of the scalar field $varphi$ is proportional to the scalar curvature of the spacetime. The equation of motion has the form like non-linear wave equation. The next step is to proof local existence of solutions. We have show that both the $k^{th}$ linear energy and energy norm are bounded for the finite time with the initial data in $H^{k+1} imes H^k$. Finally, we have prove the uniqueness and smoothness properties of the solution.