An exhaust gas heat exchanger for a cogeneration system is disclosed. In the exhaust gas heat exchanger, a heat exchanger cover is arranged around a heat exchanger body such that a primary heat medium passage, through which a heat medium passes, is defined between the heat exchanger cover and the heat exchanger body. In the heat exchanger body, a heat medium tube forming a secondary heat medium passage, through which the heat medium emerging from the primary heat medium passage passes, is arranged. Accordingly, the heat medium primarily absorbs heat from the exhaust gas while passing through the primary heat medium passage, and then secondarily absorbs heat from the exhaust gas while passing through the secondary heat medium passage. As a result, an enhancement in heat exchanging efficiency is achieved.