Abstract: The paper investigates the self-normalized large deviations for the supercritical continuous-time Markov branching process Z(t), t ≥ 0. Specifically, our study focuses on the continuous-time case and extends the conclusions drawn by Athreya¹. Additionally, we explore the self-normalized large deviation in the context of branching processes with immigration. In our analysis, we utilize the results of self-normalized large deviations for i.i.d. random variables presented in Shao².