With Euclidean Jordan algebras, we proved the level-boundedness of the merit function related to a penalized Fischer-Burmeister function for symmetric cone complementarity problems with monotonicity in a method of inner product.The method has more universality and promotion value both on theories and applications compared with previous trace inequality method to prove level-boundedness of the merit function. Level-boundedness plays an important part on a guarantee of decline algorithm convergence when we design algorithm to solve unconstrained minimization problem. Therefore, it has theoretical significance on the design of algorithm.