In this paper, we consider a three-species spatial food chain system as follows$ \begin{equation} \nonumber \begin{cases} u_t = d_1\Delta u + u(1-u)-b_1 uv, \ \quad\quad\ \ x\in \Omega, \; \; t>0, \\ v_t = \nabla \cdot(\gamma_1 (u) \nabla v)- \nabla \cdot(\chi_1(u) v \nabla u)+uv -b_2 vw -\theta_1 v - \alpha_1 v^2, \\ \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\ x\in \Omega, \; \; t>0, \\ w_t = \nabla \cdot(\gamma_2 (v) \nabla w)- \nabla \cdot(\chi_2(v) w \nabla v)+vw -\theta_2 w - \alpha_2 w^2, \\ \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\quad\quad \quad\ x\in \Omega, \; \; t>0, \\ \frac{\partial u}{\partial \nu} = \frac{\partial v}{\partial \nu} = \frac{\partial w}{\partial \nu} = 0, \ \quad\quad \quad\quad \quad\quad \ \ \ x\in\partial\Omega, \; \; t>0, \\ (u, v, w)(x, 0) = (u_0, v_0, w_0)(x), \ \ \ \ \quad x\in\Omega, \end{cases} \end{equation} $where $ \Omega\subset{\mathbb{R}}^2 $ is a bounded domain with smooth boundary. For $ i = 1, 2 $, all the parameters $ b_i, \alpha_i, \theta_i $ are positive and the functions $ \gamma_i>0 $ and $ \chi_i>0 $ satisfy $ (\gamma_i, \chi_i)\in [C^2([0, \infty))]^2. $ We first establish the global existence of classical solutions with uniform-in-time bound by using the coupling energy estimates and Moser iteration. Moreover, by constructing Lyapunov functionals, the global stability and convergence rate of steady states are established under certain conditions.