In the existing traction continuously variable transmission (CVT), half toroidal CVT (HT-CVT) is considered to have a better traction performance. However, the HT-CVT has the spin losses due to its structural limitations, which significantly influences the traction efficiency. In this paper, the kinematic qualities and contact models of a novel zero-spin rolling conical CVT (RC-CVT) are studied, and then the rollers and conical disks are compactly designed through the proposed design principles. Subsequently, the transmission efficiency is investigated by using a detailed numerical model and compared with HT-CVT. Based on these computational models and parameters, the practical spin ratio, spin momentum and traction efficiency of RC-CVT are calculated and compared with HT-CVT. The results show that the practical spin ratio and spin momentum of RC-CVT are much smaller than that of HT-CVT, and the efficiency on fixed transmission ratio is consequently higher than that of HT-CVT.