In this paper, we consider the Cauchy problem of the quasilinear
Sch\"{o}dinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t =
\Delta u+2uh'(|u|^2)\Delta h(|u|^2)+V(x)u+F(|u|^2)u+(W*|u|^2)u,\ x\in
\mathbb{R}^N,\ t>0\\ u(x,0) = u_0(x),\quad x\in \mathbb{R}^N.
\end{array}\right. \end{equation*} Here $h(s)$, $F(s)$, $V(x)$ and $W(x)$ are
some real functions. $V(x) \in L^{p_1}(\mathbb{R}^N) +
L^{\infty}(\mathbb{R}^N)$, $p_1>\max(1,\frac{N}{2}$), and $W(x)\in L^{p_2}
(\mathbb{R}^N)+L^{\infty} (\mathbb{R}^N)$, $p_2>\max(1,\frac{N}{4})$, $W(x)$ is
even. Based on pseudoconformal conservation law, we establish Morawetz
estimates and the spacetime bounds for the global solution. We also obtain
interaction Morawetz estimates for the global solution.