Tunneling plays an essential role in many branches of physics and has found important applications. It is theoretically proposed that Klein tunneling occurs when, under normal incidence, quasiparticles exhibit unimpeded penetration through potential barriers independent of their height and width. We created a phononic heterojunction by sandwiching two types of artificial phononic crystals with different Dirac point energies. The direct observation of Klein tunneling as shown by the key feature of unity transmission is demonstrated. Our experiment reveals that Klein tunneling occurs over a broad band of acoustic frequency. The direct observation of Klein tunneling in phononic crystals could find applications in signal processing, supercollimated beams, and communications.