A barrel-type multistage pump comprising: centrifugal impellers that are provided at a rotary shaft in plural stages; an inner casing that covers the centrifugal impellers, and includes diffusers that are provided on the downstream sides of the respective centrifugal impellers in plural stages, return channels that are provided on the downstream sides of the diffusers to guide the flow of a fluid to the centrifugal impeller in the next stage, and return vanes that are arranged at the respective return channels; a cylindrical outer casing that has a suction pipe with suction opening as the inlet and a discharge pipe with discharge opening as the outlet of the fluid, a cylindrical flow channel connected to the discharge opening is provided between the outer casing and the inner casing, a connecting channel provided between the cylindrical channel and the flow diffuser of the last stage to connect therebetween, wherein the connecting channel is inclined towards the suction opening side, this inclination being defined in a meridional plane by an inclined angle (α, β, γ) between the centerline of the connection channel and the center line of the discharge pipe, and wherein the axial position of an outflow position of the connecting channel in the cylindrical flow channel is located near the central line of the discharge pipe, characterized in that the connecting channel is configured such that the inclined angle (α, β, γ) changes, in particular increases, along the circumferential direction, resulting in a changing axial position of the outflow position of the connecting channel, such that along the circumferential direction, the fluid flowing out of the connecting channel is axially spread in the cylindrical flow channel. centrifugal impellers that are provided at a rotary shaft in plural stages; an inner casing that covers the centrifugal impellers, and includes diffusers that are provided on the downstream sides of the respective centrifugal impellers in plural stages, return channels that are provided on the downstream sides of the diffusers to guide the flow of a fluid to the centrifugal impeller in the next stage, and return vanes that are arranged at the respective return channels; a cylindrical outer casing that has a suction pipe with suction opening as the inlet and a discharge pipe with discharge opening as the outlet of the fluid, a cylindrical flow channel connected to the discharge opening is provided between the outer casing and the inner casing, a connecting channel provided between the cylindrical channel and the flow diffuser of the last stage to connect therebetween, wherein the connecting channel is inclined towards the suction opening side, this inclination being defined in a meridional plane by an inclined angle (α, β, γ) between the centerline of the connection channel and the center line of the discharge pipe, and wherein the axial position of an outflow position of the connecting channel in the cylindrical flow channel is located near the central line of the discharge pipe, characterized in that the connecting channel is configured such that the inclined angle (α, β, γ) changes, in particular increases, along the circumferential direction, resulting in a changing axial position of the outflow position of the connecting channel, such that along the circumferential direction, the fluid flowing out of the connecting channel is axially spread in the cylindrical flow channel.