This paper proposes a linear variable machine equipped with a set of field winding which is capable for adjusting the air-gap flux. As conventional variable reluctance machines, the proposed machine has a doubly salient structure and no permanent magnets or windings on the mover. The distinct feature of the proposed machine is that there are both the ac armature winding and the de field winding in the stator. By inviting the dc field winding, the proposed machine not only has the flux control capability, but also realizes the bipolar operation. In this paper, the proposed machine design and its operating principle are presented and discussed. Then, a two-phase machine in modular design is dimensioned. By using the three-dimensional finite element analysis, both the steady and transient performances are quantitatively analyzed and evaluated.