The symplectomorphism groups $Symp(M, \omega)$ of ruled surfaces have been started by Gromov, McDuff, and Abreu, etc, using J-holomorphic techniques. For rational ruled surfaces, the topological structure of $Symp(M, \omega)$ is better understood, while for irrational cases our only knowledge is for minimal ruled surfaces. In this talk, we focus on non-minimal ruled surfaces and prove a stability result for $Symp(M, \omega)$. As an application, we find symplectic mapping classes that are smoothly but not symplectically isotopic to identity. Time permitting, we will discuss some related conjectures. The talk is based on joint works with Olguta Buse.