Stator-magnet moving-iron transverse-flux linear oscillatory machine (SMTLOM) is a promising reciprocating drive for linear actuator due to its merits of simple structure, high reliability, low fabrication cost, etc. However, for the special topology and operation principle of SMTLOM, the asymmetric saturation would occur during its operation, which has significant influence on the electromagnetic performance. Hence, in this article, the design method for SMTLOM is presented with the full consideration on saturation effect. First, the axial-asymmetric saturation is described in detail, and consequently, the influence of such effect on the main parameters selection is investigated based on the introduced saturation coefficient. Furthermore, the demagnetization calibration is also carried out to illustrate how the axial-asymmetric saturation impacts the operation point of the magnets on flux-weaken-side stator. Finally, a prototype is manufactured and tested by both static and dynamic experiments, which have validated the theoretical analysis and simulation.