This paper investigates the properties of asymmetric gaits of a rimless wheel (RW) with knee joints. The RW consists of one point mass at the hip and eight identical massless legs with knees. Any walking patterns converge to the limit cycle which includes stance and impact phases. The mechanical energy dissipates at the heel strike and is restored by impulsive kicking control. Two types of asymmetric gaits are investigated; one is generated by two different restored mechanical energies and the other is generated by two different strides. The walking speed of the asymmetric gaits is compared with that of symmetric gaits through numerical simulations. It is shown that the constraint on the stride is necessary to realize high-speed walking.