This paper proposes a high speed QPSK/OQPSK digital burst modem which employs a reverse modulation carrier recovery scheme to recover high speed burst mode signals in low Eb/No environment. The proposed all digital high speed burst modem achieves both high speed carrier recovery and very low carrier slipping performances simultaneously which other methods cannot achieve. To achieve these performances, a carrier recovery circuit with a wave forming filter for reverse modulation of OQPSK signal is proposed to reduce operation speed and still to keep the same carrier signal-to-noise ratio, in addition, an interpolation scheme with a pulse shape filter for bit timing recovery to avoid analogue VCO and to reduce overhead for bit timing recovery. Computer simulation results show that the proposed demodulator achieves high speed carrier acquisition and a low carrier slipping rate enough to meet the required value, 1.0×10-8 event/symbol at an Eb/No of 4.1dB with negligible small bit error rate degradation. The proposed modem can be implemented in all-digital circuits and suitable for LSIC implementation.