A key challenge associated with cellular-based machine-type communication (MTC) is to provide better coverage enhancement (CE) along with low power consumption for MTC user equipments (UEs). Due to the limitation on total power allowed for transmission, it is required to estimate frequency error in very low signal-to-noise ratio condition. In this article, an effective frequency offset estimation method is presented for MTC in a long term evolution system. The proposed method applies the repetitive nature of the MTC physical broadcast channel to the weighted least-squares estimation technique. Both analytical and simulation results are provided to corroborate the feasibility of the proposed method. It is shown that the proposed estimation scheme is more efficient for CE of MTC UEs, compared to the existing method.