When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dirac point in the temperature dependent Shubnikov de Haas oscillations, which probe the 'relativistic' Dirac particle-like dispersion. The relevance of Berry's phase to these experiments is confirmed by the phase shift of magneto-oscillations, related to the exceptional topology of the graphene band structure.