Based on the effective mass theory, the conditon of normal-incidence absorption of intersubband transitions for n-type semiconductor quantum well(QW)infrared detector was derived by using the expression of matrix element of intersubband transition in the conduction band. Using some simple mathematical methods, the absorption coefficient of normal-incidence radiation can be represented as an analytical function of the growth direction of QWs.The optimization, the limitation of normal-incidence absorption and the comparison between it and parallel-incidence absorption were discussed. By considering the degeneracy and the occupancy of the ellipsoidal constant energy surface, the calculation for four kinds of QWs material was presented for the doping concentration of 1018 cm-3and detecting wavelength of 10pm.Some optimal growth directions of QWs for the largest normal-incidence absorption were proposed,which are useful for the design of the novel QWs infrared detectors.