Abstract: We propose a stable and efficient particle-based method for simulating highly viscous fluids that can generate coiling and buckling phenomena and handle variable viscosity. In contrast to previous methods that use explicit integration, our method uses an implicit formulation to improve the robustness of viscosity integration, therefore enabling use of larger time steps and higher viscosities. We use Smoothed Particle Hydrodynamics to solve the full form of viscosity, constructing a sparse linear system with a symmetric positive definite matrix, while exploiting the variational principle that automatically enforces the boundary condition on free surfaces. We also propose a new method for extracting coefficients of the matrix contributed by second-ring neighbor particles to efficiently solve the linear system using a conjugate gradient solver. Several examples demonstrate the robustness and efficiency of our implicit formulation over previous methods and illustrate the versatility of our method.