In this paper, a system of fuzzy polynomial equations is studied. Two solution types are defined for this system, called solution and \(r\) -cut solution. Then sufficient and necessary conditions are proposed for existence of solution and \(r\) -cut solution of the system, respectively. The solution set of the system is also determined. Moreover, a new algorithm is designed to find all the solutions and all the \(r\) -cut solutions of the system based on the eigenvalue method. Finally, some examples are given to illustrate the concepts and the algorithm.