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Sequential fault diagnosis is a kind of important fault diagnosis method for large scale complex systems, and generating an excellent fault diagnosis strategy is critical to ensuring the performance of sequential diagnosis. However, with the system complexity increasing, the complexity of fault diagnosis tree increases sharply, which makes it extremely difficult to generate an optimal diagnosis strategy. Especially, because the existing methods need massive redundancy iteration and repeated calculation for the state parameters of nodes, the resulting diagnosis strategy is often inefficient. To address this issue, a novel fast sequential fault diagnosis method is proposed. In this method, we present a new bottom-up search idea based on Karnaugh map, SVM and simulated annealing algorithm. It combines failure sources to generate states and a Karnaugh map is used to judge the logic of every state. Eigenvalues of SVM are obtained quickly through the simulated annealing algorithm, then SVM is used to eliminate the less useful state. At the same time, the bottom-up method and cost heuristic algorithms are combined to generate the optimal decision tree. The experiments show that the calculation time of the method is shorter than the time of previous algorithms, and a smaller test cost can be obtained when the number of samples is sufficient.