The invention belongs to the field of compressors, and discloses a multistage compressor. The multistage compressor comprises an end cap, a spindle assembly, a swash plate assembly, a cylinder block assembly, a plurality of stages of piston assemblies, air distributing valve assemblies and a plurality of connecting pipes. Each stage of piston assembly comprises a sliding shoe, a connecting rod, afirst piston, a second piston, a left limiting block and a right limiting block. The right end of each stage of piston assembly is provided with the corresponding air distributing valve assembly so that air input and air output of a compression cavity can be achieved. The multiple connecting pipes are used for connecting the air distributing valve assemblies and connecting the air distributing valve assemblies in series, so that gas flows from a cylinder liner with large inner diameter into a cylinder liner with small inner diameter, and gas compression is achieved. A swash plate structure isadopted, and multistage pistons are arranged radially and peripherally, so that the size and weight of the multistage compressor are greatly reduced.