The underwater broadband anechoic coating is highly demanded in acoustic stealth for underwater vehicles. In this work, we propose a gradient index metamaterial for broadband underwater sound absorption, which is further experimentally validated under high pressure conditions. The gradient index metamaterial consisting of radius-varied cavities in rubber allows the sound waves to follow the objective trajectory in a broad band with impedance matching at the interface with water. The viscosity of the materials and the coupling effect among the gradient cavities contribute to broadband sound absorption. The performance of broadband sound absorption from 1 to 10 kHz is validated experimentally, which agrees well with the theoretical and numerical results. We further experimentally demonstrate the sound absorption performance with hydrostatic pressure up to 3 MPa and analyze the mechanism of the sound absorption deviation caused by high pressures. The proposed gradient index metamaterial provides a simple and efficient way to develop underwater broadband acoustic coatings.