Rolling cylinder displacement compressor

A rolling cylinder displacement compressor including a minimum pressure bypass port as an opening of a minimum pressure bypass valve flow path, which is connected to a compression chamber formed in the compression portion in a lowest pressure state, of the bypass valve flow path is arranged such that a compression chamber faces an opening of the discharge flow path or the minimum pressure bypass port. The minimum pressure bypass port may be configured such that a minimum pressure port center as the center of the minimum pressure bypass port is arranged in a rotation advanced-side region with respect to an advanced radius line as a line connecting a cylinder advanced corner point of the compression chamber at the start of a compression stroke and the rotation center of the rolling cylinder.