The artificial noise (AN) aided multi-beam directional modulation (DM) technology is capable of wireless physical layer secure (PLS) transmissions for multiple desired receivers in free space. The application of AN, however, makes it less powerefficient for such a DM system. To address this problem, the weighted fractional Fourier transform (WFRFT) technology is employed in this paper to achieve power-efficient multi-beam DM transmissions. Specifically, a power-efficient multi-beam WFRFTDM scheme with cooperative receivers and a power-efficient multi-beam WFRFT-DM scheme with independent receivers are proposed based on frequency diverse array (FDA), respectively. The bit error rate (BER), secrecy rate, and robustness of the proposed multi-beam WFRFT-DM schemes are analyzed. Simulations demonstrate that 1) the proposed multi-beam WFRFT-DM schemes are more power-efficient than the conventional multibeam AN-DM scheme; 2) the transmission security can also be guaranteed even if the eavesdroppers are located close to or the same as the desired receivers; and 3) the proposed multi-beam WFRFT-DM schemes are capable of independent transmissions for different desired receivers with different modulations.