At a half-filled Landau level, composite fermions with chiral p-wave pairing will form a Moore-Read state which hosts charge- e/4 fractional excitation. This excitation supports non-Abelian statistics and has potential to enable topological quantum computation. Owing to the SU(4) symmetry of electron and electric-field tunability, the bilayer graphene becomes an ideal platform for exploring physics of multi-component quantum Hall state and is candidate for realizing non-Abelian statistics. In this work, high-quality bilayer graphene/hBN heterostructure is fabricated by using dry-transfer technique, and electric transport measurement is performed to study quantum Hall state behavior in bilayer graphene under electric field and magnetic field. Under strong magnetic field, the sequences of incompressible state with quantized Hall conductivity are revealed at –5/2, –1/2, 3/2 filling of Landau level. The feature of even-denominator quantum Hall state is more visible then weaker with increasing magnetic field, and this corresponds to the polarization of Landau level wave function. The experimental results indicate that the observed even-denominator fractional quantum Hall state belongs to the topological phase described by Pfaffian wavefunction.