Branch -like pipeline is a common structure in gas transmission pipeline. In the light of the constituent properties of natural gas branch - like pipeline system, the system can be divided into fundamental constituent units. This paper presents a realistic unsteady flow model consisting of simple models of pipeline units and connecting conditions, boundary conditions and initial condition associated with units by using system analysis method. The solutions in wide sense are obtained by theory of functional analysis and operator series method, Such a method has the properties of both analytical solution and numerical solution methods. When the divided pipeline unit is larger, an intuitive approximate analytical solution may be obtained; while the one is smaller, a more accurate numerical solution may be acquired. Based on this, a general computer program has been developed for this model and solutions have been used successfully in a local natural gas transmission network in Sichuan. It is proved that the model and algorithm proposed in this paper are of the advantages of convenient calculation, high precision, time saving and wide application range by way of analysis and application.