The invention relates to an isothermic shift reactor. The isothermic shift reactor comprises a furnace body and a catalyst frame arranged in the furnace body, wherein a shift gas collecting pipe is arranged in the middle of the catalyst frame, one port of the shift gas collecting pipe is closed, the other port is connected with the outside, and multiple gas inlets are formed in the side wall of the shift gas collecting pipe; through holes communicated with space inside and outside the catalyst frame are formed in the wall of the catalyst frame; multiple heat exchange pipes are arranged in a cavity between the catalyst frame and the shift gas collecting pipe. The isothermic shift reactor is characterized in that the heat exchange pipes are divided into multiple heat exchange pipe groups, each heat exchange pipe group comprises a first heat exchange pipe and multiple second heat exchange pipes; all the second heat exchange pipes are arranged around the corresponding first heat exchange pipe; a lower port of each first heat exchange pipe is connected with a cooling water pipeline, and a lower port of each second heat exchange pipe is connected with a steam collecting pipeline; lower ports of the first heat exchange pipes and the second heat exchange pipes are communicated with the cavity between the catalyst frame and the furnace body; upper ports of the first heat exchange pipesand the second heat exchange pipes are communicated with inner cavities of pipe caps, and the pipe caps adopt a closed cavity structure.