Abstract: Ionospheric refraction effects on VHPradio waves play an important role in space technique, such as tracking, navigation, telemetry etc. In theorical range, it has always been supposed that the ionospheric parameters are spherically symmetric except Alpert did in 1963. But Alpert's formulas only contain ionospherically first-order contribution, (ionospherical refraction effects can be expanded as power series in terms of 1/f)In this paper, based on Alpert's work (1963), a new ray diffrencial equations are given aswhere k1=R0 sin ds and ds. From this, it is easy to give expressions of ionospherical refraction effects including higher order ionospheric contribution. In consideration of the complexity of those expressions, only first three order contribution are provided.