Phasor estimates produced by the Taylor-based weighted least square filter (TWLS) can be erroneous if the reference frequency is not close to its real value. On the other hand, online calculation of the TWLS coefficients leads to the significantly increased computational cost. In this paper, a low complexity algorithm is proposed, that aims to enhance the phasor and frequency estimation at off-nominal frequencies. The proposed algorithm utilizes a symmetric TWLS (STWLS) filter to iteratively estimate the parameters of the positive image of the fundamental component. Due to the symmetry in the STWLS frequency response, an estimation accuracy at off-nominal frequencies can be significantly improved by adjusting the filter center frequency, which slightly affects the computational complexity. In a variety of scenarios, simulation results confirm the favorable performance of the proposed algorithm over the TWLS.