The first case of coronavirus disease 2019 (COVID-19) in Algeria was reported on 25 February 2020. Since then, it has progressed rapidly and the number of cases grow exponentially each day. In this article, we utilize SEIR modelling to forecast COVID-19 outbreak in Algeria under two scenarios by using the real-time data from March 01 to April 10, 2020. In the first scenario: no control measures are put into place, we estimate that the basic reproduction number for the epidemic in Algeria is 2.1, the number of new cases in Algeria will peak from around late May to early June and up to 82% of the Algerian population will likely contract the coronavirus. In the second scenario, at a certain date T, drastic control measures are taken, people are being advised to self-isolate or to quarantine and will be able to leave their homes only if necessary. We use SEIR model with fast change between fully protected and risky states. We prove that the final size of the epidemic depends strongly on the cumulative number of cases at the date when we implement intervention and on the fraction of the population in confinement. Our analysis shows that the longer we wait, the worse the situation will be and this very quickly produces.