In this paper, we propose a new frequency-switching array (FSA) to enhance the physical-layer security (PLS) in the presence of multiple eavesdroppers (Eves), where the carrier frequency can be flexibly switched and small frequency offsets can be imposed on each antenna at the secrecy transmitter (Alice).First, we analytically show that by flexibly controlling the carrier frequency parameters, FSAs can effectively form uniform/non-uniform sparse arrays, hence resembling existing mechanically controlled movable antennas (MAs) via the control of inter-antenna spacing and providing additional degree-of-freedom in the beam manipulation.Although the proposed FSA suffers from additional path-gain attenuation in the received signals, it can overcome several hardware and signal processing issues incurred by MAs, such as limited positioning accuracy, extra hardware and energy cost.Then, a secrecy-rate maximization problem is formulated under the constraints on the frequency control.To shed useful insights, we first consider a secrecy-guaranteed problem with a null-steering constraint for which maximum ratio transmission beamformer is considered at Alice and the frequency offsets are set as uniform frequency increment.Interestingly, it is shown that the proposed FSA can flexibly realize null-steering over Eve in both the angular domain and range domain, thereby achieving improved PLS performance.Then, for the general case, we propose an efficient algorithm to solve the formulated non-convex optimization problem by using the block coordinate descent and projected gradient ascent techniques. Finally, numerical results demonstrate that the proposed FSA achieves superior secrecy rate performance over conventional fixed-position array, while it only suffers a slight secrecy rate loss than the existing mechanically controlled MA.