Abstract: When the uncertainty analysis is performed for reactor physics calculation, it is often necessary to generate a multi-dimensional correlated variable pseudo-random number sequence. However, previous research shows that a particularly large sample sequence is required to basically ensure that the sample covariance matrix is consistent with the real covariance matrix. The reason why the covariance matrix of the previous multi-dimensional correlated variable pseudo-random number sequence is different from the real covariance matrix was first theoretically analyzed. The reason is that the generated multi-dimensional random number sequence is correlated. Then, the solution was proposed and verified by numerical calculation. For the sampling sequence of three variables, twenty samples were used for the high-precision correlated variable sampling method to obtain the same as the original correlation coefficient matrix. The number of sampled samples is reduced by two orders of magnitude compared with the previous method. The analysis of the ²³⁸U radiation capture reaction channel of 33 groups shows that even if the number of sampled samples is 34, the maximum relative error is only 0.061%, thus proving the method correctness. Finally, different methods for lead-based fast reactor LFR were analyzed. The total sample number of the traditional normal distribution sampling method is 1 times than that of high-precision correlated variable sampling method. The maximum relative error of the traditional normal distribution sampling method is 12.5%, and that of high-precision correlated variable sampling method is only 1.7%. Calculation accuracy is improved obviously. It shows that this method has a prospect in engineering application.