Fatigue constitutive curve is the presentation of mechanical response and damage mechanism of composites. The hysteresis phenomenon in composites is essentially attributed to the viscoelastic properties of the polymer matrix, causing the strain response to lag behind the stress excitation. Combined with the fatigue damage modes of composites, the contributions of elastic, plastic and viscoelastic strains to the cumulative cyclic strain are analyzed to determine the evolution law of the hysteresis loops with cycling. The hysteresis loops and cyclic hysteresis energy models of composites under tensile-tensile fatigue loads are proposed, and the models are verified by the experimental results of four kinds of laminates under several fatigue loads.