Genome-wide association studies (GWAS) have identified hundreds of common variants associated with alcohol consumption. In contrast, rare variants have only begun to be studied for their role in alcohol consumption. No studies have examined whether common and rare variants implicate the same genes and molecular networks. To address this knowledge gap, we used publicly available alcohol consumption GWAS summary statistics (GSCAN, N=666,978) and whole exome sequencing data (Genebass, N=393,099) to identify a set of common and rare variants for alcohol consumption. Gene-based analysis of each dataset have implicated 294 (common variants) and 35 (rare variants) genes, including ethanol metabolizing genes ADH1B and ADH1C, which were identified by both analyses, and ANKRD12, GIGYF1, KIF21B, and STK31, which were identified only by rare variant analysis, but have been associated with related psychiatric traits. We then used a network colocalization procedure to propagate the common and rare gene sets onto a shared molecular network, revealing significant overlap. The shared network identified gene families that function in alcohol metabolism, including ADH, ALDH, CYP, and UGT. 74 of the genes in the network were previously implicated in comorbid psychiatric or substance use disorders, but had not previously been identified for alcohol-related behaviors, including EXOC2, EPM2A, CACNB3, and CACNG4. Differential gene expression analysis showed enrichment in the liver and several brain regions supporting the role of network genes in alcohol consumption. Thus, genes implicated by common and rare variants identify shared functions relevant to alcohol consumption, which also underlie psychiatric traits and substance use disorders that are comorbid with alcohol use.