A syringe pump in which it is possible to reduce a length of a cover member of when the cover member is contracted and to reduce a distance between a moving member of a syringe pusher driving part and a housing part of when the moving member becomes the closest to a side of the housing part and which can be downsized is provided. A syringe pusher driving part 7 includes a boot 800 included as a cover member which covers a feed screw 135 and which can be elastically deformed and contracted as a syringe pusher pushing member 10 moves to a side of a syringe body 201. The boot 800 includes a plurality of first protruded parts 811 to 816 and at least one second protruded part 821 or 822 formed between two successively-formed first protruded parts and next two successively-formed first protruded parts. An outer diameter dimension DG1 of a connection part 990 between the two successively-formed first protruded parts is set smaller than an outer diameter dimension DG2 of a connection part 995 between the second protruded part and the first protruded part.