Traditional quaternion-based sliding mode observer for angular velocity estimating has to introduce the process of mandatory rescaling which affects the tracking performance of the observer algorithm. In this work, a sliding mode observer design framework is proposed, based on the Lie group method of numerical integration on manifolds for angular velocity estimation of quadrotor attitude. The algorithm constructs sliding mode feedback in the space of equivalent Lie algebra of homogeneous manifolds on the basis of equivariant mapping ideological. It avoids the complexity of constructing sliding mode feedback in homogeneous space directly, and eliminates the process of mandatory rescaling which is required by the traditional methods in each integration step. The simulation results show that the algorithm of geometric sliding mode observer is effective.