Fixed point problems and equilibrium problems have many applications and areefficient tools in science, engineering, analytic structures and many other fields. Theequilibrium problem in particular is a very general mathematical problem that includes manyspecial cases such as optimization problems, integral inequality problems, fixed point problems,etc. In this article, the authors will propose a weak convergent theorem for an algorithm forfinding common solutions of a pseudomonotone equilibrium problem and a finite system ofnon-extended mappings in a real Hilbert space. Almost existing methods for solving thisproblem require a strict assumption of the strong monotonicity or Lipschitz-type continuity ofthe cost bifunction f . The idea of this algorithm is to combine the projection method and theparallel splitting-up technique. At each iteration step, the authors need to use one projectiononly and do not require to use any Lipschitz-type continuity condition of the bifunction.