In most stochastic response analysis of structures with random parameters, independence or complete correlation of these parameters is assumed. It is recognized that practical random parameters are partially correlated, which may have obvious influence on the statistical properties of stochastic responses. Recently, a random function model was proposed to characterize the dependence between two random parameters. In this model, the underlying physics is introduced to yield the shape of the function, then the observed data are taken to identify the parameters of the function. On this basis, the stochastic seismic response of a concrete frame structure with dependent random strength and random initial elasticity of modulus is studied. Meanwhile, in order to capture the whole propagation path of randomness, the probability density evolution method (PDEM) is employed in this paper. The results show that when the nonlinearity of structural behavior is strong under severe earthquakes, the discrepancy between the results considering and without considering the dependence of random parameters cannot be ignored.