A heat exchanger and an indoor thermoelectric air conditioner containing the heat exchanger, the heat exchanger includes a heat transfer plate provided with an elevation area for the plate to be erected on bottom in outer casing of the air conditioner; multiple heat sink fins parallel with one another are fixed on one side of the plate at where abutted to the elevation area; free ends of those fins are inclined downward in a direction facing the elevation area; a fan blows the air from both sides of each fin to create airway between any two abutted fins; water of vapors in the air condensed on surface of each fin fall off downward due to central gravity thus to separate waterway from airway to warrant well-facilitate air vane of the air conditioner; and outer surface of each fin being applied with a hydrophilic film to frustrate condensation to further insurance of the well-facilitated air vane.