The single-cone bit has become the first choice for slim hole sidetracking and deep well drilling with its unique rock breaking method and high ROP (Rate Of Penetration), with its main failure mode being of early excessive wear of the cutting teeth. In order to improve the adaptability of single-cone bits to hard and highly abrasive formations, a spherical single-cone Polycrystalline Diamond Compact (PDC) compound bit is designed. According to the characteristics of the tooth profile, the way of tooth arrangement and the way of contact between the cutting teeth and the rock, the acceleration equation to the cutting teeth of the spherical single-cone PDC compound bit is established. The acceleration of the single-cone bit is verified by numerical simulation experiment of rock-breaking. The shaft inclination angle of the cone, the position and height of the PDC teeth, the radius of the PDC teeth, the lateral rotation angle and the front inclination angle on the acceleration are studied. The results show that as the shaft inclination angle increases, the bit transmission ratio gradually increases, and the harder the rock formation, the larger the transmission ratio of the single-cone bit; the shaft inclination angle and the position of the PDC tooth have a greater influence on the acceleration of the PDC tooth, and the radius, lateral rotation angle and front inclination angle of the PDC tooth have a small influence on the acceleration of the PDC tooth; rock properties have an impact on the acceleration of the cutting teeth, with the acceleration of the cutting teeth in hard rock formations being higher than that in soft rock formations; near the top of the cone, the absolute acceleration of the cutting teeth will fluctuate sharply and cause severe wear of the cutting teeth, so the tooth distribution in this area should be strengthened; on the premise that the bearing life of the single-cone bit is allowed, the value of the shaft inclination angle β can be approached to 70°. The relative error between the theoretical analysis results of the acceleration of the PDC cutter and the rock-breaking simulation experiment results is between −0.95% and −2.24%. This research lays a theoretical foundation for the dynamic research of spherical single-cone PDC compound bit.