This study proposes an acoustic black hole (ABH) beam with varying carbon fiber orientation and thickness for a low cut-on frequency and high stiffness. The proposed fiber-steered ABH beam contains a laminate with a varying fiber orientation as a junction between a tapered 90° laminate and uniform 0° laminate. The anisotropic viscoelastic properties of the carbon fiber-reinforced plastic were identified using dynamic mechanical analysis tests and a micromechanics model for fiber composites. An analytical model was developed to derive the solutions for the displacement field, cut-on frequency, and reflection coefficient. The analytical solutions demonstrated that varying the fiber orientation contributes to the decrease in the cut-on frequency and the reduction of the reflection coefficient while maintaining the stiffness of the host structure. Finite element method analyses were performed to investigate the frequency response of the fiber-steered ABH beam. The fiber-steered ABH beam exhibited lower resonance peaks than the uniform 0° laminate beam. The higher loss tangent of the 90° laminate compared to that of the 0° laminate improved the damping performance without an additional viscoelastic material layer. The frequency response calculated using the analytical solution agreed well with the numerical analysis results.