This paper presents a low-complexity equalization for M-ary biorthogonal keying based direct sequence ultra wideband (MBOK DS-UWB) systems. We focus on a Viterbi equalizer, which is based on maximum likelihood sequence estimation (MLSE). To reduce the computational complexity of MLSE-based equalizer, we use two strategies. One is the use of delayed-decision feedback sequence estimation (DDFSE), which is a hybrid estimation between MLSE and decision feedback estimation (DFE). And the other is the truncation of state transition in MLSE by considering MBOK pulse mapping. The reduced complexity sequence estimation is named as reduced state (RS)-DDFSE. By the use of RS-DDFSE, the complexity of Viterbi equalizer for MBOK DS-UWB is significantly reduced, by comparison with that of MLSE. The performance of RS-DDFSE based equalizer is evaluated on multipath fading channel models provided by IEEE802.15.3a. An analysis on trellis diagram of RS-DDFSE and simulation results show that the impact on error rate performance generated by the complexity lower is slight.