A self-consistent numerical model is presented for magmatism in a convecting mantle with moving plates. Mantle convection is modeled as a thermal-chemical convection of binary eutectic material with Newtonian rheology in a two-dimensional rectangular box internally heated by radioactive elements. Viscosity is assumed to depend on stress history as well as temperature and pressure to self-consistently reproduce moving plates. The barrier effect of the solid-solid phase transitions at depths around 660 km to convective flow across the 660 km phase boundary is also taken into account. Magmatism is modeled as a permeable flow of basaltic melt produced upon decompression melting of the convecting material through the coexisting matrix. Magmatism makes mantle chemically stratified with the shallower part occupied by chemically buoyant residue of magma and the deeper part occupied by hot but chemically dense materials enriched in basaltic component even under the influence of moving plates and subducting slabs. The magmatism is induced by moving plates (ridge volcanism), mantle overturn, and hot plumes uprising from the 660 km phase boundary or the lower mantle, depending upon the internal heating rate and the strength of the 660 km barrier. A weaker 660 km barrier leads to more continuous plate tectonics. When plates move, subducting slabs penetrate deep into the lower mantle and induce broad thermal and chemical heterogeneity at depth in the lower mantle. The chemically stratified mantle with moving plates is compared to the Earth's mantle.