The English online auction creates great business opportunities. However, it¡¦s different from traditional English auction in long bidding time, wide area, high risk, massive information, and low switching cost. It makes bidders easy to search information of the goods but difficult to win the auction. The bidders' transaction cost structure has changed from information phase to agreement phase. So, the bidders need more precise supporting tools to help them make decisions. The aim of this research is to investigate two-person optimal bidding strategies under three dimensions of the decision space: the sequence decision (bid firstly or later), the bid decision (bid or quit), and the jump decision (minimum increase or jump bid). It is assumed that there are two bidders competing in one auction. Variables associated with the auction system include the floor price and the minimum increase. Variables associated with the bidders include the private value of the bidding object, and the cost of bid per turn. Strategies were evaluated based on the following criteria: who wins, how many turns to win the bid, the deal price, the utility of the winner and the loser, the probability of winning, and the expected utility. The results indicate that every strategy has its advantages and disadvantages under certain conditions. This research provides guiding rules for the bidders to choose a better strategy.