This paper redefines critical reaction. It is more reasonable to demarcate reactions which may have negative reactants. Based on the definition, the accelerated ? -leap algorithm is proposed. Even if the number of some species in biochemical systems is small, the ? -leap algorithm is adaptive. This algorithm also increases the speed of simulation. The accurate stochastic simulation algorithm (SSA) algorithm, an improved ? -leap algorithm and the present accelerated algorithm are compared in two biochemical reaction models. Numerical results demonstrate that the proposed method is faster under the same simulation precision.