An evaporator having front and rear heat exchange assemblies arranged at air inlet and outlet sides, respectively, and adjacent to each other. Each heat exchange assembly includes a pair of upper and lower headers, and multiple refrigerant channels each having upper and lower ends connected to the upper header and lower headers. The upper and lower headers are internally provided with vertical partitions for internally dividing the headers into portions arranged laterally to reverse the direction of upward or rearward flow of a refrigerant through the refrigerant channels of the rear heat exchange assembly every specified number of refrigerant channels, and thereby provide at least one group of upward refrigerant channels in each of left and right halves of the rear heat exchange assembly. The evaporator can be used in a motor vehicle air conditioner.