Splicing P systems are a class of distributed parallel computing models in the framework of membrane computing, which are inspired by the recombination of DNA molecules under the influence of restriction enzymes. In this work, a variant of P machine, called splicing P machine, is presented, which can provide an automata approach to investigate splicing P systems. It is shown that such a device can do what the splicing P system does. Several examples are given to illustrate that splicing P machine can provide the same results as the corresponding splicing P system. This work provides an answer to an open problem formulated by G. Ciobaun and M. Gontineac.