The dimensions of flextensional transducers are much smaller than the wavelength, thereby constraining the generation of directional beams by compact underwater acoustic transducers. To address the complexity of amplitude and phase modulation in circuit-driven traditional directional flextensional transducers, this study proposes a directional flextensional transducer structure. By implementing an asymmetric composite shell configuration combining concave and convex curved beams, the design achieves low-frequency directional radiation while simplifying peripheral driving circuits, thereby offering enhanced operational convenience and cost-effectiveness. Beginning with an analysis of vibration characteristics and radiation mechanisms, this study reveals the directional generation principle. The concave and convex beams of the flextensional transducer exhibit an intrinsic operational characteristic of opposite-phase normal displacement in their vibration modes. By adjusting structural parameters, the amplitude output by the two beams under a single actuator drive can satisfy a specific differential relationship, effectively resulting in the modal superposition of a monopole and a dipole, thereby achieving directional radiation. Using a Lorentzian resonance fitting function and a linear fitting function, the relationship between the frequency-dependent amplitude ratio and phase difference of sound pressure for the concave and convex beams was established, forming an unequal amplitude, unequal phase dual-spherical source radiation model for the transducer. This provides a theoretical framework for controlling the directivity of the transducer. Through numerical simulations, the effects of the transducer sidewall parameters, as well as the thickness and curvature radius of the concave and convex beams, on the transducer’s resonance frequency, transmitting voltage response, front-to-back sound pressure ratio, and directivity were analyzed. Sensitivity ranking of the structural parameters was also presented. Finally, the optimized transducer's performance was discussed and compared with other existing research, demonstrating the advantages of this design. Specifically, the transducer achieves a maximum transmitting voltage response of 145.9 dB within the operating frequency band of 1240 Hz to 1660 Hz. Under single-circuit drive, it produces a cardioid-shaped directional beam with a maximum front-to-back sound pressure ratio of 27 dB. Furthermore, it significantly reduces the shear stress on the active material, effectively preventing fatigue failure of the active material during high-power emission. This provides a more convenient method for achieving low-frequency underwater acoustic directional emission.