The goal of this paper is to study the complete lift of the semi-symmetric non-metric $\phi$-connection on a Kenmotsu manifold to its tangent bundle $TM$ and to obtain a relation between the semi-symmetric non-metric $\phi$-connection $\bar{D}^C$ on Kenmotsu manifolds with respect to Levi-Civita connection $D^C$ by utilizes specialized mathematical operators. on $TM$. Next, the complete lifts of the curvature tensor, the scalar curvature and the Ricci tensor on $TM$ are constructed and show that Ricci tensor is symmetric on $TM$. Finally, a study of the complete lift of curvature tensor concerning the semi-symmetric non-metric $\phi$-connection to its tangent bundle $TM$ is done which shows that if the complete lift of the curvature tensor of $\bar{D}^C$ vanishes on $TM$, then the Kenmotsu manifold is locally isometric to the hyperbolic space $H^n(1)$ on $TM$.