This work focuses on the rapid determination of Acoustic Emission (AE) wave propagation velocity in composite laminate and sandwich structures using a closed-form formula. Firstly, a classical closed-form model proposed in the literature is extended to determine the acoustic wave velocity in any direction in a composite laminate or sandwich structure; then a corrective factor has been defined to improve the calculation accuracy; finally, a parameter, called correlation ratio has been introduced to describe the relation between acoustic wave velocity in the composite skin and that in the sandwich panel. This strategy has been validated by two types of composite sandwich panels: one is honeycomb sandwich structures with CFRP composite laminate skins; the other is balsa sandwich with GFRP skins. It is demonstrated that acoustic wave velocity in the sandwich is dominated by the skin property, namely the elastic modulus of the skin, the density of the constituents, the core and skin thickness. Moreover, only by measuring the velocity in one direction, the velocity in any direction of composite structures can be predicted accurately and quickly. This work lays the first foundations for the establishment of numerical and experimental models necessary to improve the damage localization of composite structures.