Transmit beamforming and artificial noise (AN)-based methods have been widely employed to achieve physical-layer (PHY) security. However, these approaches may fail when the channels of legitimate user (LU) and eavesdropper (Eve) are highly correlated; e.g., the Eve's channel is proportional to the LU's. The target of this work is to address the PHY security problem with directionally-aligned LU and Eve in millimeter-wave (mmWave) communications; i.e., the transmitter, Eve and LU are aligned along the same direction. To this end, we propose a novel frequency diverse array (FDA) beamforming approach to differentiating LU and Eve. The FDA beamforming intentionally introduces some frequency offsets across the antennas to generate an angle-range dependent beampattern. By exploiting its range discrimination capability, FDA beamforming can degrade Eve's reception and thus achieve PHY security. By leveraging FDA beamforming, we aim to maximize the secrecy rate by jointly optimizing the frequency offsets and the beamformer. This secrecy rate maximization (SRM) problem is difficult to solve due to the tightly coupled variables. Nevertheless, we show that it can be reformulated into a form depending on the frequency offsets only. Building upon this reformulation, we identify some cases under which the problem can be optimally solved with closed-form solution. For more general cases, we apply the block successive upper-bound minimization (BSUM) method to iteratively find a solution with stationary convergence guarantee. Numerical results demonstrate that FDA beamforming can provide much higher secrecy rate as compared with the conventional beamforming, especially for the case of highly correlated channels.