The present invention relates to a multi-stage, single reactor and system for making methanol for synthesis gas (syngas). In particular, the reactor contains a shell and tube reactor that is divided at its top and bottom heads into a plurality vertical, isolated compartments. The associated compartments and tubes form a stage of the reactor. The raw syngas is fed to the first stage, and unreacted syngas from the first stage is fed to the second stage subsequent stages. Between each stage, the product, methanol and water, is removed from the reaction mixture before sending the unreacted syngas to the subsequent stage. The reactor allows for high conversion of synthesis gas to methanol in a once-through process, without requiring recycling of unreacted synthesis gas.