The quantum effects for a physical system can be described by the set ε(H) of positive operators on a complex Hilbert space Hthat are bounded above by the identity operator Ⅰ. The infimum problem of Hilbert space effects is to find under what condition the infimum A∧B exists for two quantum effects A and B ∈ε(H). The problem has been studied in different contexts by R. Kadison, S. Gudder, M. Moreland, and T. Ando. In this note, using the method of the spectral theory of operators, we give a complete answer of the infimum problem. The characterizations of the existence of infimum A ∧ B for two effects A, B ∈ε(H) are established.