Non-orthogonal multiple access (NOMA) scheme has been recognized as a promising candidate for future generation networks. In order to achieve a superior spectral efficiency, the orthogonal frequency division multiplexing (OFDM) technique can be combined with the NOMA scheme. However, introducing OFDM into the NOMA scheme induces carrier frequency offset (CFO) errors in the system. In this paper, the impact of the CFO on the performance of the OFDM based NOMA is investigated and analyzed. Also, to improve the performance of the CFO plagued NOMA-OFDM scheme, an iterative weighted least square (WLS) algorithm is derived and implemented to achieve CFO estimation. First, the conventional least square (LS) method is used to obtain initial CFO estimates. Thereafter, a weighted LS approach is presented, where the weighting parameter is obtained using a Markov estimate. The proposed WLS algorithm utilizes the conventional LS method as its initialization point. Simulation results are presented to show the effect of the CFO errors on the NOMA-OFDM system. Also, the performance of the proposed estimation algorithm is presented and analyzed.