Evolutionary algorithms have long been quite successfully applied to solve multi-objective optimization problems. However, theoretical analysis of multi-objective evolutionary algorithms (MOEAs) is mainly restricted to the simple evolutionary multi-objective optimizer (SEMO). The Pareto archived evolution strategy (PAES) is a simple but important multi-objective evolutionary algorithm which is come from the study of telecommunication problems, and it has been successfully applied to many optimization problems, such as image processing and signal processing. In this paper, we make a first step toward studying the rigorous running time analysis for PAES. We show that the PAES outperforms the SEMO on function PATH when the PAES uses a simple mutation operator. However, it can not find the whole Pareto front with overwhelming probability on the well-studied function LOTZ. Additional experiments show that the experimental results are in agreement with the theoretical results.