Best linear unbiased predictors(BLUP) of breeding values for body weights at 18 months of age(18W) as single trait evaluation and those for 3 growth traits as multiple trait evaluation were estimated by indirect solving methods with reduced animal model(RAM) in Korean Native Cattle. Of 1629 animals reared at Korean Native Cattle Improvement Center, only 867 heads had valid records for all analytic traits. Breeding values for 18W could be estimated at 16 rounds of iteration by successive overrelaxation method with 1.4 relaxation factor and 2×10^-4 convergence criteria. In multiple trait evaluation involving birth weight(BW), weaning weight (WW) and postweaning gain(PG) with 2361 of mixed model equations, estimates by 1×10^-4 convergence criteria could be obtained at 29 rounds of iteration, when block iteration method with 1.2 relaxation factor was used, and also approximate prediction error variances could be estimated. The range of breeding values for WW was -37.5∼48.4㎏ and that for PG was -17.9∼16.6㎏ in multiple trait evaluation.