The generation of an isolated attosecond gamma-ray pulse utilizing Compton backscattering of a relativistic electron bunch has been investigated. The energy of the electron bunch is modulated while the electron bunch interacts with a co-propagating few-cycle CEP (carrier envelope phase)-locked laser in a single-period wiggler. The energy-modulated electron bunch interacts with a counter-propagating driver laser, producing Compton back-scattered radiation. The energy modulation of the electron bunch is duplicated to the temporal modulation of the photon energy of Compton back-scattered radiation. The spectral filtering using a crystal spectrometer allows one to obtain an isolated attosecond gamma-ray.