Background: Most of the mathematical modeling studies on COVID-19 transmission are based on continuous deterministic models that do not consider the characteristics of social network. Methods: The effect of contact tracing on mitigating COVID-19, and other infectious diseases in general, is studied in a small-world network. This network has its advantages over the commonly used continuous deterministic mathematical models in that the characteristics of social networks can be properly incorporated. Results: Simulation results show that for the original strain of SARS-CoV-2, contact tracing can play an important role to reduce and delay the peak daily new cases. New cases can be reduced by using symptom onset to isolate tracked individuals, but the benefit can be greatly enhanced by testing asymptomatic and pre-symptomatic individuals on the 6th to 8th day of infection. For the delta variant, or other variants of much higher infectivity, contact tracing alone cannot significantly lower the number of daily new cases but is able to delay the peaks greatly, thus affording more time to explore and implement pharmaceutical interventions. Conclusions: Contact tracing can be a very powerful tool to combat COVID-19 caused by the original strain or any variant of SARS-CoV-2. In order to make contact tracing effective, every effort is needed to expand the pool of contact tracing and provide all necessary support to the self-quarantined.