A roller compacted concrete dam (RCCD) located in Cambodia has been gradually deformed over the operation period (2011–2019), and the creep effect of the dam foundation is significant. In order to make integrity and safety assessments of the dam, it is necessary to know the actual mechanical properties of the foundation. This research proposes an intelligent computational framework for analysing the time-dependent working behaviour of the RCCD combined with viscoelastic finite element methods and advanced software techniques. According to the long-term deformation characteristics of the foundation, the Burgers model is employed to describe the constitutive relation of the bedrock. A finite element formulation describes the relationship between dam deformation and mechanical properties in the creep regime. A structural inverse methodology based on improved parallel grey wolf optimization (IGWO) is developed in order to search and identify viscoelastic parameters of the dam foundation. The nonlinear convergence factor strategy and multi-core parallel computing are introduced to enhance global search capability and improve the accuracy of the optimization algorithm. An example of analysis is performed on a dam section, and the results, which are compared with actual measurements for discussion, demonstrate that the selected constitutive model is reasonable and the designed inverse methodology is feasible. Moreover, the proposed IGWO algorithm is very competitive with other state-of-the-art optimization methods such as basic grey wolf optimization (GWO), particle swarm optimization (PSO) and whale optimization algorithm (WOA) for parameter inversion and real-time problems.