We present a study of the transmission dynamics of the COVID-19 outbreak in Pakistan. Important transmission pathways such as the role of Asymptomatic, Quarantined and Isolated individuals are incorporated in the model. The model is then used to study the outbreak in Pakistan, considering the different lockdown and social distancing measures taken at different times by the health authorities noting that the epidemic curve in Pakistan has been quite different from those in Europe and the US, with a significantly lower disease burden and mortality rate.