Concrete, a creep material between ideal solid and fluid, is related to loading age and load-bearing time. In this article, the fractional order calculus model is applied to the analysis of concrete’s creep. A fractional order creep model with five parameters is established based on the generalized Kelvin model with software components. Furthermore, according to measured creep values of three engineering cases, the five parameters of the established fractional order creep model are inverted and optimized by using the complex optimization algorithm. The expressions of concrete creep model in consideration of loading age are given. Engineering case study demonstrates that the calculated values of the fractional order model agree well with test values, close to those of eight-parameter model. Fractional order model could be a new approach in creep analysis of concrete.