A rectifier and a flowmeter, the rectifier including a fairing, wherein a first rectifying section (1) positioned at the upstream, a reducing section (2) positioned at the midstream and a second rectifying section (3) positioned at the downstream, can be arranged in the fairing. The first rectifying section and the second rectifying section are respectively provided with a group of rectifying channels parallel to the flow direction of fluid, and a through-hole (21) can be formed in the reducing section. The rectifier can provide improved rectification effects.