A metamaterial vibration isolator, termed as wave-insulating isolator, is proposed, which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation. It consists of plate-shaped metacells, whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow. The bandgap mechanisms, vibration isolation properties, effects of key parameters, and robustness to complex conditions are clarified. As experimentally demonstrated, the wave-insulating isolator can improve the vibration insulation in the ranges of [50 Hz, 180 Hz] and [260 Hz, 400 Hz] by 15 dB and 25 dB, respectively, in contrast to the conventional isolator with the same first resonant frequency.