Due to the producer-consumer dependency of shared variables, the potential parallelism embeded in the logic programming language has not been fully examined. The method proposed in this paper eliminates the dependency of shared variables by introducing number-sequenced variables in expanding an AND-OR proof tree. Basically, the execution of a logic program can be divided into two phases : expanding an AND-OR tree and proving the tree by matching facts with leaf nodes. In the course of the first phase, a set of number-sequenced variables are produced by expanding an AND-OR tree in the breadth-first searching. Based on the information of number-sequence, each of them is verified in the second phase in order to prove the tree. Consequently, the proposed algorithm can explore more parallelism without the dependency of shared variables.