An evaporator includes a plurality of flat heat exchange tubes arranged in a left-right direction at a spacing with the widthwise direction thereof pointing forward or rearward, and fins arranged between respective adjacent pairs of heat exchange tubes. The fins have at least front edges thereof projected forwardly outward beyond the heat exchange tubes. Assuming that the amount of projection of the fins beyond the heat exchange tubes is X mm and that the heat exchange tubes are Y mm in thickness in the left-right direction, i.e., in height, X and Y have the relationship of 0.11Y≦X≦1.0Y. The surfaces of the fins can be drained of condensation water efficiently.