A novel and simplified orthogonal frequency division multiplexing (OFDM) equalizer uses a coordinate rotation digital computer (CORDIC) to convert the estimated channel effects from rectangular coordinate to polar coordinate and to compensate the phase error with the same CORDIC circuit of synchronization. The OFDM equalizer comprises: a fast Fourier transformer (FFT), to conduct Fourier transformation to received signals to obtain samples of the received signals; a channel estimation circuit to estimate channel effects of a received signal as transformed by the FFT to generate a channel effect estimation value; a coordinate translator, comprising a CORDIC circuit, to translate the channel estimation value into a polar coordinate value; a pilot extractor, provided downstream to the FFT, to extract pilot signals and to track minor phase offsets of the received signal to synchronize phase of said received signal; a phase rotator to compensate phase of the received signal according to the channel estimation value and the phase tracking estimation value, to generate the real value and imaginary value of the phase compensated signal; and an amplitude adjustment circuit to adjust amplitude of the compensated signal according to the amplitude adjustment value of the channel effect estimation value of the channel estimation circuit. In the present invention, the coordinate translator and the phase rotator use the same CORDIC circuit.