<p style='text-indent:20px;'>We analyze superconvergence property of the lowest order curl-curl conforming finite element method based on polynomial preserving recovery (PPR) for the two-dimensional quad-curl problem on triangular meshes. We observe that the linear interpolation of <inline-formula><tex-math id="M1">\begin{document}$ \nabla \times \boldsymbol u_h $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M2">\begin{document}$ \boldsymbol u_h $\end{document}</tex-math></inline-formula> is the numerical solution) can be written as a linear combination of solutions of two discrete Poisson equations obtained by the usual linear finite element method. Therefore, the superconvergence analysis of the quad-curl problem can be attributed to the analysis of the Poisson equation. Then, with the help of the existing superconvergence results for the Poisson equation, we prove that recovered <inline-formula><tex-math id="M3">\begin{document}$ \nabla \times \nabla \times \boldsymbol u_h $\end{document}</tex-math></inline-formula> (by applying PPR to <inline-formula><tex-math id="M4">\begin{document}$ \nabla \times \boldsymbol u_h $\end{document}</tex-math></inline-formula>) is superconvergent to <inline-formula><tex-math id="M5">\begin{document}$ \nabla \times \nabla \times \boldsymbol u $\end{document}</tex-math></inline-formula>. Based on this superconvergent result, we derive an asymptotically exact <i>a posteriori</i> error estimator. Numerical tests are provided to demonstrate effectiveness of the proposed method and confirm our theoretical findings.</p>