A geometry-based three-dimensional (3D) novel stochastic channel model for air-to-ground (A2G) and ground-to-air (G2A) radio propagation environments is proposed. The vicinity of a ground station (GS) is modelled as surrounded by effective scattering points; whereas the elevated air station’s (AS) vicinity is modelled as a scattering-free region. Characterization of the Doppler spectrum, dispersion in the angular domain and second order fading statistics of the A2G/G2A radio communication channels is presented. Closed-form analytical expressions for joint and marginal probability density functions (PDFs) of Doppler shift, power and angle of arrival (AoA) are derived. Next, the paper presents a comprehensive analysis on the characteristics of angular spread on the basis of shape factors (SFs) for A2G/G2A radio propagation environments independently in both the azimuth and elevation planes. The analysis is further extended to second order statistics of the fading channel; where the behaviour of the level crossing rate (LCR), average fade duration (AFD), auto-covariance and coherence distance for the A2G/G2A radio propagation environment is studied. Finally, the impact of physical channel parameters, such as the mobility of AS, the height of AS, the height of GS and the delay of the longest propagation path, on the distribution characteristics of Doppler shift, angular spread and second order statistics is thoroughly studied.