<p>In this work, periodic solutions of a three-dimensional chaos laser system, which externally injected class <i>B</i> which is described by a system of three nonlinear ordinary differential equations with two parameters for field intensity phase and population inversion, are studied. The first order of the method of averaging theory is applied for determining and analyzing the bifurcating periodic solutions from a Hopf—zero equilibrium point localizing at the equilibrium point coordinates. We show that exist only one parameter family of the laser system for which the equilibrium point is a zero Hopf bifurcation point. We prove that, at most, one non-hyperbolic limit cycle bifurcates from the zero-Hopf equilibrium. Moreover, we perform a global dynamical analysis of a flow of system at infinity using Poincare’s compactification and local stability of equilibrium points. We describe its dynamic on the Poincare sphere at infinity in detail via the Poincare compactification, showing unstable and stable nodes at the endpoints of the z-axis.</p>