Abstract: In order to study influence of natural convection during melting of phase change material,the oscillatory phenomenon of natural convection was investigated.With enthalpy-porosity method and Boussinesq hypothesis,single-phase governed equations were set up and simulation on melting process under gravity was completed.It is shown that when the Rayleigh number Ra is small,the natural convection can be obtained with a steady solution,then the flow changes from a steady state to a periodical oscillatory state with the increase of Ra.