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Differential orthogonal space-time modulation (DOSTM) with amplitude/phase shift keying (APSK) signals has been proposed to improve the throughput of the DOSTM with phase shift keying (PSK) signals over quasi-static channels. In this paper, decision feedback differential detection (DF-DD) based on linear prediction is presented for the DOSTM with APSK signals (DOSTM-APSK) over frequency-non-selective fading channels. The proposed DF-DD offers better performance than the DD when the channel experiences fast fading. The coefficients of the linear prediction based DF-DD can be obtained by an adaptive RLS algorithm, where the channel statistics is not needed. The proposed DF-DD is also applicable to the general unitary differential space-time modulation (DSTM).