We have provided model-based estimates of Covid-19 in the U.S. during April–June 2020. The newly reported Covid-19 cases of April in the U.S. have not acquired the virus in the same month. We estimate that there was an average of 29,000/day Covid-19 cases in the U.S. transmitted from infected to susceptible during April 1–24, 2020, after adjusting for under-reported and under-diagnosed. We have provided model-based predictions of Covid-19 for the low and high range of transmission rates and with varying degrees of preventive measures including the lockdowns. We predict that even if 10% of the susceptible and 20% of the infected who were not identified as of April 30, 2020 do not adhere to proper care or do not obey lockdown, then by the end of May and by end of June 50,000 and 55,000 new cases, respectively, will emerge. These values for the months of May and June with worse adherence rates of 50% by susceptible and infected (but not identified) will be 251,000 and 511,000, respectively. Continued and serious lockdown measures could bring this average daily rate of new cases to a further low with a range of 4,300/day to 8,000/day in May.