Fast switching speed, low power consumption, and good stability are some of the important properties of spin transfer torque assisted voltage controlled magnetic anisotropy magnetic tunnel junction (STT-assisted VCMA-MTJ) which makes the non-volatile full adder (NV-FA) based on it attractive for Internet of Things. However, the effects of process variations on the performances of STT-assisted VCMA-MTJ and NV-FA will be more and more obvious with the downscaling of STT-assisted VCMA-MTJ and the improvement of chip integration. In this paper, a more accurate electrical model of STT-assisted VCMA-MTJ is established on the basis of the magnetization dynamics and the process variations in film growth process and etching process. In particular, the write voltage is reduced to 0.7 V as the film thickness is reduced to 0.9 nm. The effects of free layer thickness variation (γ_tf) and oxide layer thickness variation (γ_tox) on the state switching as well as the effect of tunnel magnetoresistance ratio variation (β) on the sensing margin (SM) are studied in detail. Considering that the above process variations follow Gaussian distribution, Monte Carlo simulation is used to study the effects of the process variations on the writing and output operations of NV-FA. The result shows that the state of STT-assisted VCMA-MTJ can be switched under -0.3%≤γ_tf≤6% or -23%≤γ_tox≤0.2%. SM is reduced by 16.0% with β increases from 0 to 30%. The error rates of writing ‘0’ in the NV-FA can be reduced by increasing V_b1 or increasing positive V_b2. The error rates of writing ‘1’ can be reduced by increasing V_b1 or decreasing negative V_b2. The reduction of the output error rates can be realized effectively by increasing the driving voltage (V_dd).