Common variants at many loci have been robustly associated with asthma but explain little of the overall genetic risk. Here we investigate the role of rare (<1%) and low-frequency (1–5%) variants using the Illumina HumanExome BeadChip array in 4,794 asthma cases, 4,707 non-asthmatic controls and 590 case–parent trios representing European Americans, African Americans/African Caribbeans and Latinos. Our study reveals one low-frequency missense mutation in the GRASP gene that is associated with asthma in the Latino sample (P=4.31 × 10⁻⁶; OR=1.25; MAF=1.21%) and two genes harbouring functional variants that are associated with asthma in a gene-based analysis: GSDMB at the 17q12–21 asthma locus in the Latino and combined samples (P=7.81 × 10⁻⁸ and 4.09 × 10⁻⁸, respectively) and MTHFR in the African ancestry sample (P=1.72 × 10⁻⁶). Our results suggest that associations with rare and low-frequency variants are ethnic specific and not likely to explain a significant proportion of the ‘missing heritability’ of asthma.