A continuously variable transmission (CVT) with an inner spherical traction drive was conceptually designed for bicycle usage. The range of the overall speed ratio is from 1.0 to 4.5. The rated power and pedal speed are 100 Watts and 6 rad/s, respectively. The peculiar packageability, high-level power efficiency and high torque capacity were considered in the design process. A compact CVT that can be installed within a $244 imes125 imes160mm^3$ space and is above 0.9 in efficiency for the rated values was numerically designed. The distribution of efficiency according to the input torque and input speed were calculated. Gradeability in the prescribed operation mode was simulated.