An energy-conserving reduced kinetic model is formulated which is valid for perturbations with large amplitude and long wavelength beyond the standard gyrokinetic ordering. The standard gyrokinetic model is elegantly formulated by the two-step phase space transformation consisting of the guiding-center and gyro-center transformations, but the amplitude of perturbations is assumed to be small in return for use of the two-step transformation. Besides, the wavelength of perturbations is assumed to be short in deriving the gyrokinetic Poisson equation. Both limitations are relaxed by using the modified guiding-center 1-form for flowing plasmas [Miyato et al., J. Phys. Soc. Jpn. 78, 104501 (2009)].