High-quality broadband ultrasound transducers yield superior imaging performance in biomedical ultrasonography. However, proper design to perfectly bridge the energy between the active piezoelectric material and the target medium over the operating spectrum is still lacking. Here, we demonstrate a new anisotropic cone-structured acoustic metamaterial matching layer that acts as an inhomogeneous material with gradient acoustic impedance along the ultrasound propagation direction. When sandwiched between the piezoelectric material unit and the target medium, the acoustic metamaterial matching layer provides a broadband window to support extraordinary transmission of ultrasound over a wide frequency range. We fabricated the matching layer by etching the peeled silica optical fibre bundles with hydrofluoric acid solution. The experimental measurement of an ultrasound transducer equipped with this acoustic metamaterial matching layer shows that the corresponding -6 dB bandwidth is able to reach over 100%. This new material fully enables new high-end piezoelectric materials in the construction of high-performance ultrasound transducers and probes, leading to considerably improved resolutions in biomedical ultrasonography and compact harmonic imaging systems.