•We report a familial cluster of COVID-19 to assess potential transmission of the disease during the incubation period.•A familial cluster of four patients with COVID-19 in Zhoushan, China had contact with an asymptomatic family member, who developed symptoms later.•The infectivity during the incubation period for SARS-CoV-2 is a big challenge for controlling the disease. We report a familial cluster of 2019 novel coronavirus disease (COVID-19) to assess its potential transmission during the incubation period. The first patient in this familial cluster was identified during the presymptomatic period, as a close contact of a confirmed patient. Five family members had close contact with this first patient during his incubation period, with four of them confirmed positive for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection in the subsequent sampling tests.