The local minimum problem of SPDS algorithm—the training algorithm of BP neural network, is studied. As one of SPDS algorithm features based on the single parameter dynamic searching algorithm is that the variables are searched one by one, this paper proves that the equivalence error function of each iteration is a quasi-convex function, and minimum points are presence and can be found out. The initial value set from which the iterative must be convergence is defined as the global minimum area, and according to the local minimum problems, L-SPDS algorithm is given. The global minimum area of the SPDS algorithm expanding along coordinate direction is the global minimum area of L-SPDS algorithm. The possibility that SPDS algorithm converges to the global minimum point greatly increases, which is proved by algorithm simulation test.