Norovirus is a highly transmissible infectious agent that causes epidemic gastroenteritis in susceptible children and adults. Norovirus infections can be severe and can be initiated from an exceptionally small number of viral particles. Detailed genome sequence data are useful for tracking norovirus transmission and evolution. To address this need, we have developed a whole-genome deep-sequencing method that generates entire genome sequences from small amounts of clinical specimens. This novel approach employs an algorithm for reverse transcription and PCR amplification primer design using all of the publically available norovirus sequence data. Deep sequencing and de novo assembly were used to generate norovirus genomes from a large set of diarrheal patients attending three hospitals in Ho Chi Minh City, Vietnam, over a 2.5-year period. Positive-selection analysis and direct examination of protein changes in the virus over time identified codons in the regions encoding proteins VP1, p48 (NS1-2), and p22 (NS4) under positive selection and expands the known targets of norovirus evolutionary pressure.