In wireless communication systems, Rice factor ratio (RFR) defined as K/(1+K) is a key parameter not only to evaluate the quality of communication channel since it can reveal the severity of the small-scale fading, but also to be employed as a priori information for estimation of other parameters such as frequency. Consequently, its estimation is important for a variety of wireless application scenarios. In this paper, we propose an estimation algorithm on the RFR for the received signals that are disturbed by the Rician doubly selective fading channels and additive noise. During the estimation periods, we initially utilize the known signals to multiply the received signals. Second-order and fourth-order statistics are then employed to further deal with the processed signals mentioned above, which disposes of influence of some unnecessary parameters, e.g., indistinguishable multipaths, maximum Doppler shift, Doppler shift, and noise variance. Finally, a useful expression on the RFR estimation is derived for the Rician frequency selective fast fading channels by flexibly mathematical calculation. Furthermore, the presented method only uses the maximum estimation values of the second-order and fourth-order statistics defined in this paper, which can reduce the computational complexity. Importantly, the investigated scheme is robust to the signal-to-noise ratio over 0 dB and frequency offset (maximum Doppler shift and Doppler shift), and shows a slight improvement on the estimation performance with an increase of the aided data length. The performance and benefits of the proposed approach are verified and evaluated through computer simulations.