The invention provides a shell-and-tube heat exchanger with external tube boxes. The shell-and-tube heat exchanger comprises a tube plate, a shell, heat exchange tubes, the inlet external tube box and the outlet external tube box. The outlet external tube box and the inlet external tube box are fixed to the corresponding positions of the tube plate. A flow diversion device is arranged in each of the outlet external tube box and the inlet external tube box. A cavity is formed in the middle of each flow diversion device. Multiple flow diversion runners are formed from the middle positions to the peripheries along the corresponding cavities. All the flow diversion runners extend to the tube plate, and joints corresponding to the heat exchange tubes in a one-to-one manner are formed; and a cavity in the outlet external tube box is connected with a tube side outlet tube, and a cavity of the inlet external tube box is connected with a tube side inlet tube. The shell-and-tube heat exchanger with the external tube boxes is reasonable in design and capable of effectively improving the airtightness of the heat exchanger and reducing the tube side pressure reduction and has the wide application prospects.