Spatial variability of tensile strength, widely existing in concrete gravity dams due to the influence of long construction period and heterogeneous construction quality, has a profound impact on the nonlinear behaviour of structures. In this paper, a method to simulate the random field of the tensile strength of concrete gravity dams based on the random field theory is proposed. A typical non-overflow dam section of the Guandi gravity dam is taken as an example, artificial seismic waves with similar response spectra and natural seismic waves with different magnitudes are selected for the comparative analysis. Based on the concrete damage plasticity (CDP) model and incremental dynamic analysis (IDA) method, the damage characteristics, failure modes, probability density evolution processes, and fragility curves obtained from gravity dams with homogenous and random fields of tensile strength are compared with each other. The differences among waves and realisations of random fields are also investigated. It is seen that the spatial variability of tensile strength aggravates the damage degree, decreases the continuity of local damaged areas, and increased the failure probability of global dams. It reveals that the random characteristics affect the dams’ nonlinear behaviour directly.