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This paper proposes a new design of a linear oscillating actuator (LOA) with rectangular topology of stator and mover. The shape of a permanent magnet (PM) has a major impact on cost, mechanical strength and generation of magnetic flux density. This design uses rectangular PMs that are relatively cheaper than tubular PMs. Proposed LOA operates on single phase AC loading source. All the design parameters are optimized by using parametric sweep and the response of the LOA in terms of thrust force is compared. The Electromagnetic (EM) force received by the mover is investigated at various mover positions as well as at different values of the current. Motor constant is examined toward both directions of the force. Resonance phenomena is analyzed using input and output power of the LOA, which is the unique advantage of the LOA. Compared to the conventional LOA designs, the output parameters of the LOA, such as EM force, stroke, operating frequency and power, show great improvement with regards of volume of the proposed LOA. This topology shows significant development in terms of thrust force, motor constant, easy manufacturing and cost. Moreover, range of the stroke of proposed LOA is feasible for linear refrigeration system.