The disclosure provides a vibration isolation structure for linear oscillating motor and Stirling engine, wherein the said vibration isolation structure comprises a first vibration isolation device and a second vibration isolation device. The first vibration isolation device is set between the fixed hood and the housing of the linear oscillating motor to attenuate the high-frequency and small-amplitude vibrations from the linear oscillating motor. The first vibration isolation device comprises a first set of tension springs and a second set of tension springs, and a lateral gap is formed between the fixed hood and the linear oscillating motor. The second vibration isolation device is set in the said lateral gap to attenuate the low-frequency and large-amplitude vibrations from the linear oscillating motor. The second vibration isolation device comprises at least two sets of position-limiting protrusions and position-limiting blocks, and the position-limiting protrusion and position-limiting block are set in a match at the linear oscillating motor and the fixed hood respectively or reversely. Also disclosed is a Stirling engine assembled with a linear oscillating motor that comprising with an aforementioned vibration isolation structure. The vibration isolation structure improves the stability of the reciprocating linear oscillating motor and the Stirling engine, and reduces mechanical vibrations and noises.