The invention discloses a band gap adjustable type phononic crystal vibration isolator based on shape memory alloy and relates to a vibration isolator. The band gap adjustable type phononic crystal vibration isolator based on shape memory alloy aims to solve the problems of existing one-dimensional phononic crystal vibration isolators that the periodicity of period materials is low, vibration isolating effect is poor, working space is limited, the band gap can not be adjusted, and the vibration isolation frequency range is narrow. The band gap adjustable type phononic crystal vibration isolator comprises a vibration input support, lateral skin, upper skin, lower skin, a secondary vibration isolation upper support, a vibration output support, a primary vibration isolation lower support, three primary vibration isolation phononic crystal support pillars, three secondary vibration isolation phononic crystal support pillars, three trinary vibration isolation phononic crystal support pillars, three sets of primary vibration isolation shape memory alloy compression driving components, three sets of secondary vibration isolation shape memory alloy compression driving components, three sets of trinary vibration isolation shape memory alloy compression driving components, three sets of primary vibration isolation phononic crystal components, three sets of seconday vibration isolation phononic crystal components and three sets of trinary vibration isolation phononic crystal components. The band gap adjustable type phononic crystal vibration isolator is used for vibration isolation and noise reduction.