The Grushin operator is defined as $G:=-\Delta-|x|^2\partial_t^2$ on $\mathbb{R}^{n+1}$. We study the boundedness of the multipliers $m(G)$ of $G$ on $L^p(\mathbb{R}^{n+1})$. We prove the analogue of the Hormander-Mihlin theorem for $m(G)$. We also study the boundedness of the solution of the wave equation corresponding to $G$ on $L^p(\mathbb{R}^{n+1})$. The main tool in studying the above is the operator-valued Fourier multiplier theorem by Lutz Weis.