Computing identity-by-descent sharing between individuals connected through a large, complex pedigree is a computationally demanding task that often cannot be done using exact methods. What I present here is a rapid computational method for estimating, in large complex pedigrees, the probability that pairs of alleles are IBD given the single-point genotype data at that marker for all individuals. The method can be used on pedigrees of essentially arbitrary size and complexity without the need to divide the individuals into separate subpedigrees. I apply the method to do qualitative trait linkage mapping using the nonparametric sharing statistic S(pairs). The validity of the method is demonstrated via simulation studies on a 13-generation 3028-person pedigree with 700 genotyped individuals. An analysis of an asthma data set of individuals in this pedigree finds four loci with P-values <10(-3) that were not detected in prior analyses. The mapping method is fast and can complete analyses of approximately 150 affected individuals within this pedigree for thousands of markers in a matter of hours.