This paper aims to present the design of a new 3D-printed continuously variable transmission (CVT) developed for an electric vehicle prototype competing in Shell Eco-marathon electric battery category, a world-wide energy efficiency competition sponsored by Shell. The proposed system is composed of a polymeric conic geared friction wheel assembled in the motor axle and directly coupled to the rear tire of the vehicle. The conical shape allows to implement a continuous variation of the geared friction wheel diameter in contact with the tire. The motor with the geared friction wheel was mounted over a board with linear bearings, allowing the speed ratio to change by moving the board laterally. A computational simulation model of a prototype electric vehicle with the proposed 3D-printed CVT was created in Matlab/Simulink environment to obtain the traction force in the geared friction wheel and also to analyze the vehicle performance. The simulation results demonstrated possibilities of increasing vehicle speed range output and available torque in the rear traction wheel. Also, it is shown with the simulated model that the designed CVT consumes 10.46% less energy than a fixed transmission ratio, demonstrating the CVT concept’s potential for battery consumption reduction. Lastly, a 3D-printing slicing software with an optimization algorithm plug-in was used to determine the best printing parameters for the conic geared friction wheel based on the tangential force, maximum displacement and safety factor. When compared to the original part with a 100% infill density, the optimized solution reduced the component mass by about 12% while maintaining safe mechanical resistance and stiffness.