In the calculation of the failure probability of corroded oil and gas pipelines, there are two layers of correlation between random variables and corrosion defects. In view of the insufficient research on the influence of correlation in the reliability evaluation of corroded oil and gas pipelines, this study proposes a method for calculating the failure probability of corroded oil and gas pipelines considering the influence of the two layers of correlation. In the method, the Copula function is employed to sample the random variables with correlation, and the failure probability of a single corrosion defect is calculated by using the failure limit state equation. Then, the system reliability theory is used to calculate the failure probability of corroded oil and gas pipelines with multiple corrosion defects considering the correlation between defects. Moreover, taking the actual data of a natural gas pipeline in China as an example, the Latin hypercube sampling method was used to study the influence of the two layers of correlation and the number of defects on the failure probability of the pipeline. Moreover, the effects of random variable correlation coefficient and corrosion defect correlation coefficient on the failure probability of corroded oil and gas pipelines were quantified based on sensitivity analysis. The results show that the influence of defect correlation on pipeline failure probability calculation is significantly higher than that of random variables. The probability of leakage and burst failure of small holes in corroded pipelines decreases with the increase of the correlation coefficient between defects, and increases with the increase of the number of defects. The correlation of random variables has no effect on the probability of leakage of small holes in the pipeline, and the probability of pipeline burst failure decreases with the increase of the correlation coefficient between wall thickness and pipeline diameter, and increases with the increase of the correlation coefficient of initial defect length and depth. The increase of the correlation coefficient of the axial and radial growth rate of defects has a bidirectional effect on the probability of pipeline burst failure, and the probability of pipeline burst failure increases with the increase of the correlation coefficient in the first 16 years of the prediction cycle, and decreases after about 25 years with the increase of the correlation coefficient. The research results are suitable for the analysis of the reliability evaluation of oil and gas pipelines with multiple corrosion defects which have reference significance for the safe operation of pipelines and the stable supply of oil and gas resources.