The random spread-spectrum technology is widely used in the Buck-Boost converter to reduce electromagnetic interference and the output voltage and current ripple,but it ignores the abundantly nonlinear phenomena. This paper analyzes the random spread-spectrum technology and the Buck-Boost converter accurate discrete iterative model,and explores the nonlinear phenomena of the Buck-Boost converter with random spread-spectrum technology. The bifurcation diagrams of the inductance current as the circuit parameter changes are drawn through the MATLAB programming,which proves that it has the plentiful nonlinear phenomena. It analyzes that spread-spectrum technology influence on nonlinear phenomena of Buck-Boost converter. In the context of the same circuit parameters,it discusses Buck-Boost converter bifurcation and chaotic phenomena in frequency with different range of random spread-spectrum technology. It provides theoretical foundation to circuit design.