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Corrosion of steel girders in-service is essentially a random process, therefore, the corrosion depths have time- and spatiality-varying characteristics. However, only corrosion depth in single steel girder could be acquired by the measuring method available, and the joint distribution pattern of corrosion depths within the entire structural system is still unknown, which may result in unrealistic reliability estimates on the corroded bridge system. A steel-concrete composite bridge was selected as an object, the Gamma random process model was firstly established to simulate the growth of corrosion depth in each girder, and this simulation model was further verified by observations. Then, Kendall rank correlation coefficient was used to demonstrate the correlation ships of corrosion depths in steel girders, and the calculation equation was derived for the time-dependent resistance of corroded girders. Finally, based on the Copula function, the computation approach of failure probability was developed for bridge system, taking into consideration the spatial correlation of corrosion in girders, and the system failure probability with or without the corrosion correlation were compared. The results show: in the early operation stage, this kind of spatial correlation has few effects on structural performance, but in the middle and later periods, the system reliability will be remarkably affected when corrosion depths are highly correlated. The research proposed a method to quantify the corrosion correlation among steel girders, and developed the reliability assessment method with higher accuracy for steel-concrete composite bridge system, which could provide a reference for the time-dependent reliability evaluation of composite bridge systems. [ABSTRACT FROM AUTHOR]