The creep behavior is one of the key issues in the design and construction of hydraulic concrete structures. However, it is an enormous challenge to accurately predict the development of creep deformation in concrete structures. Since the creep deformation behavior of concrete under long-term load action originates from the interaction between creep and damage, a new creep damage coupling model was developed by introducing the damage variable into the creep constitutive equation. This model utilized the statistical damage theory framework and assumed that the damage variable follows the random distribution described by the Weibull function. Then Weibull distribution parameters F0 and m were derived to determine the evolution equation of the damage variable D. Considering stress under complex stress conditions may change, the stress-strain correlation of concrete under complex stress conditions was deduced using the elastic creep theory. Moreover, the results of uniaxial compressive concrete creep tests with the corresponding numerical simulations under different levels of sustained loads, and the accuracy and applicability of the creep damage coupling model were verified. Consequently, the nonlinear creep properties of hydraulic concrete were analyzed by combining it with acoustic emission techniques.