For pedigree-based quantitative trait loci (QTL) association analysis, a range of methods utilizing within-family variation such as transmission-disequilibrium test (TDT)-based methods have been developed. In scenarios where stratification is not a concern, methods exploiting between-family variation in addition to within-family variation, such as the measured genotype (MG) approach, have greater power. Application of MG methods can be computationally demanding (especially for large pedigrees), making genomewide scans practically infeasible. Here we suggest a novel approach for genomewide pedigree-based quantitative trait loci (QTL) association analysis: genomewide rapid association using mixed model and regression (GRAMMAR). The method first obtains residuals adjusted for family effects and subsequently analyzes the association between these residuals and genetic polymorphisms using rapid least-squares methods. At the final step, the selected polymorphisms may be followed up with the full measured genotype (MG) analysis. In a simulation study, we compared type 1 error, power, and operational characteristics of the proposed method with those of MG and TDT-based approaches. For moderately heritable (30%) traits in human pedigrees the power of the GRAMMAR and the MG approaches is similar and is much higher than that of TDT-based approaches. When using tabulated thresholds, the proposed method is less powerful than MG for very high heritabilities and pedigrees including large sibships like those observed in livestock pedigrees. However, there is little or no difference in empirical power of MG and the proposed method. In any scenario, GRAMMAR is much faster than MG and enables rapid analysis of hundreds of thousands of markers.