We obtain a 2-dimensional area-preserving map to study the dynamical evolution of comets. The presence of singularities in the energy-increment function leads to the Levy flight random walks for the comet energies, which results in a linear increment of the energy with time. A model of stochastic dynamical system is proposed according to the map of the comet motion, which shows the existence of strong super-diffusive random walks so that the variance of the distributions can grow with time n as n 2 m with m>=1/2.