Provided are an extreme ultraviolet (EUV) exposure apparatus for improving an overlay error in a EUV exposure process, and an overlay correction method and a semiconductor device fabricating method using the exposure apparatus. The EUV exposure apparatus includes an EUV light source; a first optical system configured to emit EUV light from the EUV light source to an EUV mask; a second optical system configured to emit EUV light reflected from the EUV mask to a wafer; a mask stage; a wafer stage; and a control unit configured to control the mask stage and the wafer stage, wherein, based on a correlation between a first overlay parameter, which is one of parameters of overlay errors between layers on the wafer, and a second overlay parameter, which is another parameter, the first overlay parameter is corrected through correction of the second overlay parameter.