This paper reports the discovery of an unconventional quantum Hall effect (QHE) in bilayer graphene, characterized by a Berry's phase of 2π, which is distinct from the conventional QHE observed in two-dimensional semiconductor systems and the relativistic counterpart in single-layer graphene. In bilayer graphene, charge carriers are chiral fermions with a parabolic energy spectrum but exhibit a Berry's phase of 2π, affecting their quantum dynamics. The Landau quantization of these fermions results in Hall conductivity plateaus at standard integer positions, but the zero-level plateau is missing. This anomaly is accompanied by metallic conductivity in low concentration and high magnetic field regimes, contrasting with the conventional insulating behavior. The unconventional QHE in bilayer graphene arises from the coupling between its two layers, transforming massless Dirac fermions into chiral quasiparticles with a parabolic spectrum and a Berry's phase of 2π. This leads to a double degeneracy of the lowest Landau level, resulting in a double step in the Hall conductivity and a broader peak in longitudinal conductivity. The observed behavior is explained by the double spin and valley degeneracy in bilayer graphene, leading to a double Landau level degeneracy. The study used bilayer graphene films obtained by micromechanical cleavage of natural graphite, and measured the QHE behavior using multiterminal field-effect devices. The results show that the QHE in bilayer graphene differs from conventional systems in the absence of the zero-level plateau and the presence of a double step. The findings reveal the existence of massive chiral fermions with a Berry's phase of 2π, which are distinct from other known quasiparticles. The observation of finite metallic conductivity in bilayer graphene poses a challenge for theoretical models.This paper reports the discovery of an unconventional quantum Hall effect (QHE) in bilayer graphene, characterized by a Berry's phase of 2π, which is distinct from the conventional QHE observed in two-dimensional semiconductor systems and the relativistic counterpart in single-layer graphene. In bilayer graphene, charge carriers are chiral fermions with a parabolic energy spectrum but exhibit a Berry's phase of 2π, affecting their quantum dynamics. The Landau quantization of these fermions results in Hall conductivity plateaus at standard integer positions, but the zero-level plateau is missing. This anomaly is accompanied by metallic conductivity in low concentration and high magnetic field regimes, contrasting with the conventional insulating behavior. The unconventional QHE in bilayer graphene arises from the coupling between its two layers, transforming massless Dirac fermions into chiral quasiparticles with a parabolic spectrum and a Berry's phase of 2π. This leads to a double degeneracy of the lowest Landau level, resulting in a double step in the Hall conductivity and a broader peak in longitudinal conductivity. The observed behavior is explained by the double spin and valley degeneracy in bilayer graphene, leading to a double Landau level degeneracy. The study used bilayer graphene films obtained by micromechanical cleavage of natural graphite, and measured the QHE behavior using multiterminal field-effect devices. The results show that the QHE in bilayer graphene differs from conventional systems in the absence of the zero-level plateau and the presence of a double step. The findings reveal the existence of massive chiral fermions with a Berry's phase of 2π, which are distinct from other known quasiparticles. The observation of finite metallic conductivity in bilayer graphene poses a challenge for theoretical models.