A high speed spectral domain optical coherence tomography based on the spatial sinusoidal phase modulation for the elimination of complex-conjugate artifact is presented, where sinusoidal phase modulation of reference arm (M scan) and transverse scanning of sample arm (B scan) are performed simultaneously (sinusoidal B-M method). Herein, the linear phase modulation of the reference arm in conventional linear B-M method is modified to sinusoidal phase modulation. The proposed sinusoidal B-M method relaxes the requirements on the phase-shifting mechanical system and avoids sensitivity fall-off along the transverse direction in contrast to the linear B-M method. A criterion for the relation between transverse over-sampling factor and modulation frequency for optimal complex conjugate rejection is deduced and verified by experiments. Under this criterion, the complex spectral interferogram is reconstructed by harmonic analysis and digital synchronous demodulation. Double imaging depth range on fresh shrimp at A-scan rate of 10 kHz with complex conjugate rejection ratio up to 45 dB is achieved.