The invention relates to a flat plate crossing-flow heat exchanger. The heat exchanger comprises a shell and a heat exchange core arranged in the shell, wherein opposite angles of the heat exchange core are connected by a cross connecting piece, and the heat exchange core is closely fixed on the side wall of the shell by a fixing piece; and a plurality of closed spaces are formed between the shell and the heat exchange core. The air flow mode is that: air enters the closed space for outside circulation form an outside circulation air inlet and then returns to the outside from an outside circulation air outlet; and the air enters the closed space for inside circulation from an inside circulation air inlet and then returns to the inside from an inside circulation air outlet, and by using the temperature difference between the air in the inside and the outside, the process that the air in the inside and the outside exchanges energy is completed. The flat plate crossing-flow heat exchanger has the advantages of reasonable structural design, convenient assembly and use, low cost and high unit heat-exchange efficiency.