There is an increasing need for an independent terrestrial navigation system, owing to the increasing reliance on global navigation satellite systems (GNSS). The medium-frequency range (MF R-Mode) system is considered a promising alternative; however, the skywave effect caused by ionospheric changes at night can degrade its positioning accuracy. To address this problem, we developed an algorithm to detect and mitigate the skywave effect on MF R-Mode signals. The proposed algorithm was tested using data collected from Continuously Operating Reference Stations (CORS) monitoring the MF R-Mode signals. The skywave detection algorithm is based on the signal-to-noise ratio (SNR) induced by the groundwave and skywave composition, whereas the skywave mitigation algorithm was derived from the I and Q components of the signals obtained through IQ modulation. The results demonstrate a significant improvement in the precision and standard deviation of the range estimation using CW1 and CW2 signals. The standard deviations decreased from 39.01 and 39.28 m to 7.94 and 9.12 m, respectively, while the precision (2-sigma) increased from 92.12 and 79.82 m to 15.62 and 17.84 m, respectively. These findings confirm that the proposed algorithms can enhance the accuracy and reliability of MF R-Mode systems.