The paper discusses the continuous-time Markov branching system. We deal only with the noncritical case. The primary task of this paper is to extend to the continuous case of our recent result, which explicitly calculates the famous constant in the theory of subcritical Galton-Watson branching systems, announced by Kolmogorov in 1938. We demonstrate the convergence rate to the Kolmogorov constant for the continuous-time Markov branching system. This result contributes to determining the speed of approximation rate in several classical limit theorems of the theory of Markov branching systems.