To simulate the outgassing of CO2 and water from Martian mantle, I used a two-dimensional numerical model of magmatism in the convecting mantle. The mantle is internally heated by incompatible heat-producing elements (HPEs) that decay with time. Mantle convection is driven by thermal, compositional, and melt-buoyancy. Mantle convection causes magmatism, that is, a decompression melting of upwelling mantle materials and upward permeable flow of the generated basaltic magma through the convecting mantle. Water is incompatible and concentrates to magma in a partially molten region, while there is a saturation limit for CO2 in magma that depends on the oxygen fugacity. Water and CO2 in magma are transported upward to the surface by migrating magma and are outgassed to the atmosphere when they ascend to the top of the mantle. Both water and CO2 reduces the solidus temperature and the viscosity of solid mantle materials. The calculated mantle evolves in four stages: in Stage I, an extensive magmatism forms the crust and compositionally differentiates the mantle; in Stage II, the resulting compositional stratification of the mantle suppresses magmatism and mantle convection for tens to hundreds of millions of years to allow heat to build up in the deep mantle; in Stage III, magma is generated at depth, and the buoyancy of generated magma induces plumes that ascend through the stratified mantle to cause an episodic magmatism; in Stage IV, the magmatism subsides due to extraction of HPEs from the mantle by the magmatism itself. The episodic magmatism in Stage III outgasses water and CO2. The total amount of outgassed water is typically 100-200 m GEL (global equivalent layer), while that of outgassed CO2 is around 105 Pa s or less, when the oxygen fugacity of the mantle is in the range of Iron-Wustite (IW) buffer to one log-unit higher. This amount of CO2 is not large enough to account for the clement surface environment of early Mars by itself even when H2O enhances the greenhouse effect of CO2. Other greenhouse gasses or a remnant of the CO2 that was supplied at the time of planetary formation may have played an important role in realizing the surface environment of early Mars that was favorable to life.