Although sliding mode control (SMC) provides powerful control performance, it exhibits chattering phenomena that can lead to operational issues in quadrotor systems when certain thresholds are reached. To address this limitation, this study introduces second-order sliding mode control (SOSMC), which significantly reduces chattering. Furthermore, a modified version of the SOSMC, called advanced second-order sliding mode control (ASOSMC), is proposed by incorporating an additional term to enhance its control capabilities. The ASOSMC exhibits a stability higher than that of traditional SOSMC during quadrotor flight. We established the stability of the ASOSMC system using a more powerful strict Lyapunov stability analysis instead of the conventional Lyapunov stability employed in SMC. This paper presents the design and performance evaluation of the ASOSMC via simulation and compares it with those of conventional SMC (CSMC) and SOSMC. The simulation results confirm that the ASOSMC offers superior control performance in quadrotor systems.