Traditional additive manufacturing (also known as 3D printing) of continuous carbon fiber reinforced plastic (CCFRP) lacks the ability to manufacture parts with high speed and energy efficiency. This is mainly because of the contact needed and the slow heat transfer from the conventional hotend to the composite filaments. A microwave heating assisted additive manufacturing method is here presented which allows manufacturing CCFRP with a higher speed as compared to conventional methods. The permittivity of printed specimens with different fiber volume fraction was investigated. By using the measured dielectric properties, a micro-scale microwave radiation and heat transfer model between the fiber and resin matrix has been established. The skin-core temperature difference of the moving CCFRP filaments during conventional thermal and microwave heating has been simulated to reveal the relationship between the temperature difference, filament diameter and printing speed. Non-isothermal crystallization behavior and mechanical strengths of thermal and microwave printed specimens have been studied, and the reasons for the different results have been analyzed.