By using global ring winding, the torque coefficient of the transverse flux machine (TFM) is proportional to its number of pole pairs, and thus the TFM possesses high torque density ability when compared with other electrical machines. As a special kind of TFM, the claw pole machine (CPM) can have more torque due to its special claw pole teeth. The manufacturing of CPM or TFM with silicon steels was very difficult in the past, and is a handicap for the progress of this kind of machine. Thanks to the advent of soft magnetic composite (SMC) materials, the manufacturing process of CPM has become more and more simple. More attention has been paid to this kind of technology, and some mass production CPMs with SMC cores have appeared. However, there are few works that discuss the key design issues for this kind of machine. In this paper, a small CPM with SMC is used as as a research benchmark. Various design methods that can be adopted to improve its performance have been studied, including unequal stator claw pole teeth, a skewing magnet design, consequent pole design, and etc. The 3D finite element method (FEM) is used for the machine analysis, and it is verified by the experimental results of a CPM with SMC cores.