A healthy sucking reflex is essential for newborn calves to ensure sufficient colostrum intake in the first few hours postpartum. In recent decades, European Brown Swiss breeders have repeatedly reported that some calves lack the ability to consume colostrum directly after birth due to an absent sucking reflex. In this study, we collected the phenotypes of more than 5,500 German Brown Swiss calves and performed variance component estimation with sire threshold models using Markov chain Monte Carlo algorithms. The 50K (777K) genotypes of nearly 2,000 (200) calves were collected, and an imputation was performed for all 50K genotypes up to 777K. Genome-wide association studies (GWAS) for the trait sucking reflex were conducted for all 777K genotypes. Depending on the trait coding, a low heritability was estimated to range from 0.08 to 0.11. The GWAS results identified 34 trait-associated SNP on 6 different chromosomes. Post-GWAS analyses showed significant overrepresentation of Gene Ontologies for central nervous development and several regulative processes. Functional annotation clustering and pathway analysis revealed relations to lipid metabolism, immune and endocrine systems, and signal transduction. The results of this study suggest that breeding for an improved sucking reflex is possible but requires large data sets for the estimation of reliable breeding values (either large progeny testing groups or a large reference genome in a genomic selection program).