Abstract: In this paper, we present a novel SPH framework to simulate incompressible fluid that satisfies both the divergence- free condition and the density-invariant condition. In our framework, the two conditions are applied separately. First, the divergence-free condition is enforced when solving the momentum equation. Later, the density-invariant condition is applied after the time integration of the particle positions. Our framework is a purely Lagrangian approach so that no auxiliary grid is required. Compared to the previous density-invariant based SPH methods, the proposed method is more accurate due to the explicit satisfaction of the divergence-free condition. We also propose a modified boundary particle method for handling the free-slip condition. In addition, two simple but effective methods are proposed to reduce the particle clumping artifact induced by the density-invariant condition.