Acoustic metamaterials can manipulate sound waves in surprising ways, which include collimation, focusing, cloaking, sonic screening and extraordinary transmission. Recent theories suggested that imaging below the diffraction limit using passive elements can be realized by acoustic superlenses or magnifying hyperlenses. These could markedly enhance the capabilities in underwater sonar sensing, medical ultrasound imaging and non-destructive materials testing. However, these proposed approaches suffer narrow working frequency bands and significant resonance-induced loss, which hinders them from successful experimental realization. Here, we report the experimental demonstration of an acoustic hyperlens that magnifies subwavelength objects by gradually converting evanescent components into propagating waves. The fabricated acoustic hyperlens relies on straightforward cutoff-free propagation and achieves deep-subwavelength resolution with low loss over a broad frequency bandwidth.