We discuss the possibility of the quantum Hall effect at the half-filled,landau level in terms of pairing of composite fermions. In the absence of Coulomb energy, we show that the ground state of the system is described by the p-wave BCS pairing state of composite fermions. When the ratio alpha equivalent to (e(2)/epsilon l(B))/epsilon(F) (l(B) is the magnetic length and epsilon(F) is the Fermi energy of the composite fermions) is larger than a critical value alpha(c) similar to 8.2, the gap of the pairing state vanishes. alpha remains less than alpha(c), if h omega(c) >> e(2)/epsilon l(B) holds. In this situation the pairing state which results in the quantum Hall effect can occur. The effects of the real spin degrees of freedom and the Zeeman energy are also discussed. [S0031-9007(98)07483-3].